Chris D Lowe
email: clowe@liv.ac.uk

Laura E Martin

Emily C Roberts

Phillip C Watts

Emma C Wootton

David J S Montagnes

Collection, isolation, and culturing strategies for Oxyrrhis marina

Keywords: model protist, axenic culturing, Intraspecific variation Model protist, Axenic culturing, Intraspecific variation

The heterotrophic marine flagellate Oxyrrhis marina, is a popular and tractable model organism, being common in the intertidal environment and relatively straight forward to maintain in the laboratory. In this report, based on our experience of collecting and culturing ~400 isolates, we provide a quantification of how 'easy' O. marina is to locate and isolate from the environment and subsequently maintain in culture. In addition, we provide a brief review of the literature pertaining to O. marina culturing, stressing in particular the broad physiological tolerance and wide diet range of this organism. Finally, in light of the increasing interest in the genetics and genomics of O. marina, and heterotrophic protists more generally, we highlight existing strategies for culturing heterotrophs for '-omic' applications, and summarise our specific culturing approaches, for genomic and proteomic studies of O. marina. In this context, we outline a simplified version of Droop's medium for axenic culturing and offer details on the use of heat-killed Escherichia coli as a simple and robust food source for culturing O. marina in the absence of other eukaryotes and live prokaryotes.

INTRODUCTION

Protist experimental models should be robust and, therefore, easy to culture. Furthermore, they should be abundant and easy to isolate from the environment, such that experimental observations can be compared between replicate isolates. Finally, model organisms should be interesting and relevant tools to address fundamental biological, ecological and evolutionary questions (Montagnes et al., this issue).

The heterotrophic marine flagellate, Oxyrrhis marina, has proved to be a popular model organism, as demonstrated by the broad scope of the literature concerning this protist (e.g. Flynn and Davidson 1993;Buskey et al. 1998;Lowe et al. 2005[START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF]Saldarriaga et al. 2003, Slamovits et al. 2007). It is also apparent that O. marina is a tractable 'lab rat'.

Indeed, two commonly stated anecdotes about this species are that it is easy to grow and it is abundant in the environment. Striking features from the literature are that O. marina has broad environmental tolerances (e.g. Droop 1959;Lowe et al. 2005), and an exceptional range of prey types support its growth (see Supplementary Table 1 and references therein).

Nevertheless, despite the common use of O. marina in laboratory studies, explicit reports of culturing strategies and growth requirements are scarce, with the exception of Droop's studies (Droop, 1959a, b;Droop and Doyle, 1966;Droop and Pennock, 1971) and other brief reports scattered throughout the literature. A reassessment and synthesis of methods associated with O. marina culturing is, therefore, timely.

The second observation, that O. marina is abundant and easy to locate in the environment, is certainly anecdotal, as explicit studies examining its abundance and distribution are rare. Oxyrrhis marina is undoubtedly widespread: ~50-80 isolates are reported in the literature from a broad range of locations [START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF]. However, estimates of the effort required to obtain isolates from the environment are absent from the literature. Given that recent studies on O. marina indicate extensive genetic and phenotypic Oxyrrhis marina is commonly described as cosmopolitan and abundant in coastal habitats; the interested reader is directed to Watts et al. (this issue) for an analysis of O. marina distributions. Most reports describe O. marina from coastal environments, particularly supralittoral tide pools on rocky shores (e.g. Droop, 1953;[START_REF] Jonsson | Tidal rhythm of cyst formation in the rock pool ciliate Strombidium oculatum Gruber (Ciliophora, Oligotrichida): a description of the functional biology and an analysis of the tidal synchronisation of encystment[END_REF][START_REF] Johnson | Physical control of plankton population abundance and dynamics in intertidal rockpools[END_REF], salt marshes, estuaries [START_REF] Johnson | Microzooplankton grazing on Prorocentrum minimum and Karlodinium micrum in Chesapeake Bay[END_REF], and coastal embayments [START_REF] Begun | A "bloom" in the water of Amursky Bay (Sea of Japan) caused by the dinoflagellate Oxyrrhis marina Dujardin, 1841[END_REF]; though some of the earliest reviews of the taxon described O. marina as most commonly occurring in saltwater aquaria [START_REF] Kofoid | The free-living unarmored dinoflagellata[END_REF]. These observations are for the most part anecdotal; indeed explicit studies on the abundance and distribution of O. marina are relatively rare and limited in scope (though see [START_REF] Johnson | Physical control of plankton population abundance and dynamics in intertidal rockpools[END_REF][START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF]. Thus, whether our current understanding of distributions and abundance is driven by sampling bias or is a genuine reflection of O. marina distribution in the environment is difficult to determine.

Nevertheless, the frequency with which O. marina has been collected from coastal habitats certainly suggests abundance: ~40 isolates are described in the literature (see Lowe et al., this issue), and a further 38 were detailed in a recent study by [START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF] -all of these were isolated from coastal, and almost exclusively intertidal, habitats. However, a quantification of how easy, or not, O. marina is to recover from such habitats is absent from the literature. As part of an ongoing three-year study into the distribution of O. marina, we have undertaken an extensive sampling program, focusing primarily on northern European and Mediterranean waters, but also collecting globally. Currently, ~1000 environmental samples have been collected (Watts et al., this intertidal samples (Fig. 1a). Second, sampling effort has a clear affect on the recovery O. marina from a given location (Fig. 1b). Typically, we collect between one and ten 50 ml samples from a location, though up to 70 samples have been collected from a single site, and 160 samples were collected at one time from a 2 km shoreline in North Wales, UK. Where a single sample is collected from a given intertidal location (e.g. a stretch of shoreline), there is on average a ~40% chance of finding O. marina; the probability of collecting at least one positive sample increases to 90-100% if >10 samples are collected from one shore (e.g. samples from different tide pools; Fig. 1c). Of course, these figures are estimates and depend on the habitats sampled. Predominately, our samples have been collected from littoral pools on rocky shores, though we have also isolated O. marina from estuaries, salt marshes, coastal lagoons, and marinas. Nevertheless, a summary of our sampling data provides a useful guideline for researchers wanting to isolate O. marina. Our recommendation is that the collection of 10-20 50-ml samples from an intertidal habitat (especially a rocky shore with littoral pools) will provide a high probability of obtaining O. marina.

Finally, seasonality in O. marina abundance undoubtedly occurs. Periodic sampling of a tide-pool at Port St. Mary, Isle of Man revealed peaks in abundance in May-June then late September-October, interrupted by periods of scarcity in midsummer and winter [START_REF] Kimmance | The interactive effects of temperature and food concentration on growth responses of aquatic protists, with particular reference to the heterotrophic dinoflagellate Oxyrrhis marina[END_REF]; but also see Fig. 4 in Watts et al., this issue). We have predominately sampled in the northern hemisphere during the spring and summer; nevertheless, samples taken during the winter months (when O. marina abundance is relatively low) have also yielded isolates; thus, it can be obtained from the environment throughout the year (Fig. 1b).

Isolation and establishment of clonal cultures

The above observations support the notion that O. marina is relatively straightforward to locate in coastal habitats. Once collected, cultures are also simple to establish, as O. marina is large enough (15-40 µm long, Fig. 2) to be manipulated using finely drawn Pasteur pipettes. Common single cell isolation strategies can then be used to generate clonal cultures (e.g. [START_REF] Stein | Handbook of phycological methods[END_REF][START_REF] Kemp | Handbook of Methods in Aquatic Microbial Ecology[END_REF]. In our laboratory, we typically screen environmental samples using stereo dissection microscopes (Fig. 2); for a description of the gross morphology of O. marina see Lowe et al. (this issue). When O. marina is detected, individual cells are transferred to single wells in 24-well (2 ml) tissue culture plates with ~5 × 10 4 cells ml -1 of the autotrophic flagellate Dunaliella primolecta as food. In cases where O. marina is not immediately detected, environmental samples are inoculated with D. primolecta and re-screened 7 to 14 d later (i.e. O. marina initially present in samples at low concentrations may be undetected -an incubation period with food often allows cells to increase to detectable levels; note though that any mesozooplankton present in samples should be removed as they graze both O. marina and their prey). Monoclonal cultures can be established following three or four rounds of single cell isolation over a period of two to four weeks. In our experience, on average, 40% of isolated cells divide successful and generate moderately dense (~10 3 cells ml -1 ) cultures-though in a small number of cases all single cell isolations from a sample may die (Fig. 1d).

OXYRRHIS AS A LABORATORY ORGANISM

Undoubtedly, O. marina has become a useful experimental model organism because it is relatively easy to isolate from the environment (as highlighted above) and simple to maintain in the laboratory. This robustness is a result of broad tolerances to a range of environmental variables and an exceptionally wide diet range (Supplementary Table 1) -including the ability to maintain population growth on a fully derived cell-free medium (Droop and Pennock 1971). Below we summarise our strategy for the maintenance of O. marina stock cultures, as an indication of basic culturing requirements (at the time of writing, we maintain ~150 isolates in our laboratory; subcultures may be obtained by contacting the corresponding author). We then briefly examine the breadth of physiological tolerances in O. marina and assess its nutritional requirements.

Routine maintenance

Once established, O. marina is straightforward to maintain in the laboratory. We follow culturing methods described in much of the literature for growing temperate marine protozoa (see [START_REF] Kemp | Handbook of Methods in Aquatic Microbial Ecology[END_REF]. Briefly, stock cultures of autotrophic flagellates (e.g. D. primolecta; see Nutritional requirements, below) obtained from a commercial culture collection (e.g. Culture Collection of Algae and Protozoa, Dunstaffnage, Scotland) are grown in sterilised 32 PSU artificial seawater or filtered natural seawater; both water types are enriched with f/2 medium [START_REF] Guillard | Culture of phytoplankton for feeding marine invertebrates[END_REF] -commercially available from Sigma). We do not generally attempt to make our stock cultures of prey or O. marina bacteria free, and undoubtedly O. marina augments its diet with these bacteria [START_REF] Jeong | Feeding and grazing impact by small marine heterotrophic dinoflagellates on heterotrophic bacteria[END_REF]. Both prey and O. marina cultures are exposed to 24 h irradiance, at ~50 µmol photons m -2 s -1 , at 15-20 °C; note though that light cycle and temperature will alter growth rates (e.g. Jakobsen and Strom, 2004;Kimmance et al., 2006). Oxyrrhis marina is maintained on prey flagellates at ~10 5 cells ml -1 .

Typically, cultures are kept in ~75 ml flasks and transferred every four weeks. Using this strategy we have maintained a collection of 150-200 stock cultures for >12 months with a ~5% failure rate (i.e. 5% of the stock cultures have died).

Physiological tolerance

Oxyrrhis marina is robust to a number of parameters that may change in culture collections.

We briefly outline these below.

Salinity

Temperature

Based on previously unpublished data for 10 isolates, O. marina can survive between 10 and 30 °C, with optimal temperatures occurring between 20 and 25 °C (Fig. 3, unpublished data). These estimates agree with data from Droop (1959a) on isolate CCAP 1133/5. He indicated an optimum temperature for growth of 22.5 °C, with higher temperatures inducing rapid decreases in growth rate and mortality ensuing at temperatures >30 °C.

pH

Only two studies have investigated the pH range that O. marina can tolerate (Droop, 1959a;Pedersen and Hansen, 2003). This species has a surprisingly wide pH tolerance; it can grow between pH 7.8 -9.8. It does, however, suffer rapid mortality below pH 7.5.

Intraspecific variation

Oxyrrhis marina isolates differ genetically [START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF] and physiologically; this includes variation in responses to temperature (Fig. 3), and salinity (Lowe et al., 2005). Thus, the physiological ranges indicated above are likely to exceed the tolerances of many individual strains and, as a result, should be treated as guidelines.

Nutritional requirements

Oxyrrhis marina consumes an exceptionally broad range of prey species and food items covering a wide size range (Fig. 4, Supplementary Table 1). Although O. marina is capable of feeding on bacteria [START_REF] Jeong | Feeding and grazing impact by small marine heterotrophic dinoflagellates on heterotrophic bacteria[END_REF], the most common prey fed to O. marina during culturing are protists on the order of 10 to 50% its size (most commonly taxa in the genera Isochrysis, Dunaliella, and Rhodomonas (Fig. 4, Supplementary Table 1). For a detailed description of prey and prey preference in O. marina, see Roberts et al. (this issue).

In addition to phagotrophy, Oxyrrhis marina can be maintained on an entirely derived, cell-free medium. Extensive work, predominately by Droop in 1950s-70s (Droop, 1959a, b;Droop and Doyle, 1966;Droop and Pennock, 1971) established that O. marina could grow by osmotrophy (i.e. uptake of dissolved nutrients alone). Droop and Pennock (1971)

Culturing challenges for the 'omic era'

As a result of its phylogenetic position, basal to the dinoflagellates, and a suite of highly unusual cytological, genetic and genomic features, O. marina is increasingly the target of genetic and genomic studies aimed at understanding the evolutionary development of major protist taxa (Saldarriaga et al., 2003;[START_REF] Cavalier-Smith | Protalveolate phylogeny and systematics and the origins of Sporozoa and dinoflagellates (phylum Myzozoa nom. nov.)[END_REF]Slamovits et al., 2007; F o r P e e r R e v i e w Slamovits and Keeling 2008;[START_REF] Zhang | mRNA editing and spliced-leader RNA trans-splicing groups Oxyrrhis, Noctiluca, Heterocapsa, and Amphidinium as basal lineages of dinoflagellates[END_REF]. Advances in genome sequencing technologies mean that even for poorly characterised organisms, such as O. marina, largescale genome and transcriptome sequencing projects can be undertaken de novo [START_REF] Hudson | Sequencing breakthroughs for genomic ecology and evolutionary biology[END_REF][START_REF] Vera | Rapid transcriptome characterization for a nonmodel organism using 454 pyrosequencing[END_REF].

There is, of course, a technical issue associated with genetic and genomic studies of heterotrophic protists: heterotrophy typically necessitates using prey that also contain DNA-RNA-protein; thus, such projects begin with a 'built-in' contaminant. The extent of the problem is application-dependent; in small-scale genetic studies a known contaminant is simple to deal with. For example, gene-or locus-specific PCR and sequencing strategies can easily be adapted to cope with contaminants by designing organism-specific PCR primers or by size selection or cloning. However, for larger scale sequencing applications, the presence of contaminating prey organisms can be problematic. For example -"next generation" sequencing technologies allow de novo large-scale sequencing of organisms for which there is no prior genetic information [START_REF] Hudson | Sequencing breakthroughs for genomic ecology and evolutionary biology[END_REF]. In such cases, the presence of contaminating organisms in genome scale sequencing projects absorb sequence reads (increasing cost) and, more critically, can be impossible to separate from target sequence, confounding downstream analyses. Clearly then, strategies to generate 'clean' DNA/RNA are required to take advantage of next generation sequencing applications.

We have employed three strategies for dealing with prey contamination in O. marina cultures to generate 'clean' material for mid to large scale sequencing applications. Below we summarise these and highlight some of their advantages and disadvantages for specific applications.

Prey depletion

The simplest strategy for overcoming the presence of contaminating genetic material is to allow prey to be depleted. In our experience, in the absence of light, O. marina can graze autotrophic protists (e.g. Dunaliella spp., Isochrysis galbana) functionally to extinction. The presence, or absence, of algal cells can be determined by microscopical observations, or using PCR-based assays. For example, PCR primers designed against the 3'end of the 18S and 5'-end of the 28S rDNA genes (to amplify the 5.8S ITS rDNA region) produces 430 and 620 bp PCR fragments for O. marina and D. salina, respectively (for primer details see Lowe et al., 2005[START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF]. Thus, the presence of algal cells can be determined by simple PCR and gel electrophoresis.

As an example of the above method, for a recent study developing a microsatellite library in O. marina, we generated 500 ml cultures at densities of 4.0-5.5 × 10 4 cells ml -1 .

Cultures were established at 1 × 10 3 cell ml -1 of O. marina and 5 × 10 5 cell ml -1 D. primolecta. After 11 d (maintained in the dark at 16 to 20 °C), cultures appeared free of prey, but an rDNA PCR based assay was positive for D. primolecta. Cultures were subsequently confirmed, by PCR, to be prey-free 17 d after the initial setup. Analysis of 64 candidate microsatellite loci produced one that appeared to originate from D. primolecta (i.e. produced a positive result in a D. primolecta control PCR assay - Lowe et al., submitted). This illustrates that a simple prey depletion strategy can generate 'clean' O. marina DNA for genome scale analyses.

Live and heat-killed Escherichia coli

An alternative to the prey depletion strategy is to use a prey organism that has a known (i.e. sequenced) and small genome. The advantage is that any DNA sequence subsequently generated can be screened against a reference genome for the prey organism and removed from further analysis. Oxyrrhis marina will grow on cultures of naturally occurring marine bacteria (e.g. [START_REF] Jeong | Feeding and grazing impact by small marine heterotrophic dinoflagellates on heterotrophic bacteria[END_REF]; though clearly, the use of an undefined (and likely complex) natural bacterial assemblage does not solve the problem of identifying contaminating sequences. Instead, the use of a well-characterised bacterium, such as E. coli, has proved useful in our laboratory. Oxyrrhis marina has been demonstrated to graze E. coli cells (e.g. Kato et al., 2000), and the use of heat-killed bacteria as prey (as employed by e.g. [START_REF] Gurijala | Effect of growth rate and hydrophobicity on bacteria surviving protozoan grazing[END_REF][START_REF] Landry | Discrimination between living and heat-killed prey by a marine zooflagellate, Paraphysomonas vestita (Stokes)[END_REF]) means that prey numbers can easily be controlled. A further advantage, for mRNA and cDNA based applications is that the contribution of E. coli cells to subsequent RNA preparations will be minimal as bacterial cells are dead and thus inactive.

Our protocol for feeding O. marina with E. coli is, briefly, as follows. Cultures of E. coli (e.g. JM109, Promega) are grown in 50 to 500 ml Luria-Bertani broth at 37 ºC in an orbital incubator (210 rpm) for 8 to 12 h and culture growth monitored via optical density (following standard protocols; Sezonov et al., 2007). Cells are pelleted by centrifugation and washed twice in sterile filtered seawater (SFSW). They are then resuspend in 5 to 50 ml SFSW (~10 × concentration based on the initial volume of E. coli culture) and heat-killed at 65 °C for 30 min. Cells can be ultrasonicated, to reduce clumping and limit the occurrence of bacterial flock in the final culture. The final concentration of the preparation can be estimated based on optical density (we standardise our heat killed bacteria, HKB, stock solutions to ~2.5 -5.0 × 10 8 cells ml -1 ). A supply of 250 µl HKB in 50 ml (~1.25 -2.5 × 10 6 cells ml -1 ) of culture every 3 to 4 d will maintain O. marina in exponential growth and generate cell densities up to 1.5 × 10 5 O. marina ml -1 . Treatment with antibiotics to control naturally occurring bacteria in cultures is essential for use of this feeding strategy; we use a penicillin and streptomycin solution (100 µg ml -1 ) and treat with gentamycin (50 µg ml -1 ) during routine sub-culturing at 1-2 week intervals.

A simplified axenic medium

Research by Droop and co-workers (Droop, 1959a,b;Droop and Doyle, 1966;Droop and Pennock, 1971) indicated that O. marina can be grown indefinitely on a medium containing solely water soluble factors, highlighting that O. marina does not rely exclusively The commercial availability of readymade culture media and nutritional supplements has allowed us to simplify Droop's original axenic medium (see Table 1). Our experiments with Droop's Finnish strain of O. marina (CCAP 1133/5) and two other strains (44_PLY01, [START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF]and CCMP 1788) generated cell densities up to 1.5 × 10 5 cells ml -1 in axenic culture using our modified recipe (Table 1). Microscopical observations showed that the cells were morphologically similar to those grown on a phytoplankton diet. In addition, the axenic cells contained similar quantities of lipid and membrane protein (200 µg membrane protein, 10 7 cells -1 ) as their phytoplankton raised counterparts (Wootton, pers. obs). However, one notable discrepancy occurred: strain CCMP 1788 lost its pink pigmentation during axenic culture and the cells became opaque and white. Despite this, the cells remained active and otherwise morphologically indistinguishable from other cultures (Wootton pers. obs). We have not pursued the causes of pigmentation loss in this strain under axenic culturing, though clearly the occurrence of differences in strain responses is notable in context with other observations of genetic and physiological diversity within O. marina (Lowe et al., 2005[START_REF] Lowe | Patterns of genetic diversity in the marine heterotrophic flagellate Oxyrrhis marina (Alveolata: Dinophyceae)[END_REF].

The success of growing visibly 'healthy' O. marina cells under axenic conditions increases the potential utility of this protist as a valuable model organism, highlighting the organism's robustness. Further, this procedure overcomes problems associated with DNA-RNA-protein contamination inherent in the genetic and genomic study of heterotrophic protists. marina is likely to be a useful target for the study of a large range of questions in an ecological, physiological and evolutionary context. For example, the relatively large numbers of O. marina strains that can be practically isolated (10 2 -10 3 ) lends this organism to the study of population level processes and parameters, such as dispersal and geneflow, effective population size and adaptation -parameters and processes that are poorly characterised for free-living protists in general [START_REF] Martiny | Microbial biogeography: putting microorganisms on the map[END_REF][START_REF] Caron | Protists are microbes too: a perspective[END_REF].

It is notable from nutritional and ecophysiological studies that O. marina is incredibly flexible in its feeding requirements -able to consume a broad range of prey items but also to feed by osmotrophy. Thus, while the process of culturing is most often a means to an end, it is clear that for O. marina, explicit culturing studies to examine the physiological and biochemical basis of feeding mechanisms and nutrition are likely to be interesting avenues for future research (such directions are examined in more detail by Roberts et al., this issue).

Oxyrrhis marina also displays broad environmental tolerances; in particular, it is eurytopic with regard to salinity, temperature and pH. However, there is some evidence for ecophysiological differences between strains; thus, the study of large numbers of isolates may prove useful to assess functional diversity and processes of environmental adaptation. Finally, in light of the increasing interest in the study of the genetics, genomics and proteomics of O. marina we highlight three strategies employed in our laboratories for generating DNA/RNA/protein suitable for such applications. In particular we highlight the use of heat killed E. coli as a useful, robust, and above all, simple strategy for generating O. marina cultures free of other eukaryotic organisms. Beyond the technical challenges associated with culturing, however, the task of developing genomic resources for O. marina still remains; studies describing novel chromosome structure [START_REF] Triemer | A unique mitotic variation in the marine dinoflagellate Oxyrrhis marina (Pyrrophyta)[END_REF]Gao and Li, 1986), unusual RNA editing mechanisms (Slamovits et al., 2007;[START_REF] Zhang | mRNA editing and spliced-leader RNA trans-splicing groups Oxyrrhis, Noctiluca, Heterocapsa, and Amphidinium as basal lineages of dinoflagellates[END_REF], and potentially enormous genome size [START_REF] Sano | Localization and copy number of the protein-coding genes Actin, α-Tubulin, and HSP90 in the nucleus of a primitive dinoflagellate, Oxyrrhis marina[END_REF], suggest that the development of such resources is likely to be a complex and time consuming process. Quail yolk 2 Kato et al. (2000), [START_REF] Osaka | The protozoa dinoflagellate Oxyrrhis marina contains selenoproteins and the relevant translation apparatus[END_REF] Rhodomonas baltica 1 [START_REF] Mariani | A numerical investigation of the impact of turbulence on the feeding rates of Oithona davisae[END_REF] Rhodomonas salina 4

Carvalho and Granéli (2006), [START_REF] Chu | Quantitative significance of n-3 essential fatty acid contribution by heterotrophic protists in marine pelagic food webs[END_REF], Pedersen and Hansen (2003), [START_REF] Tang | Trophic modification of food quality by heterotrophic protists: species-specific effects on copepod egg production and egg hatching[END_REF] Rhodomonas sp. 7 Bartemeus et al. (2003), [START_REF] Grossi | Formation of phytadienes in the water column: myth or reality?[END_REF], [START_REF] Hansen | Grazing in the heterotrophic dinoflagellate Oxyrrhis marina: size selectivity and preference for calcified Emiliania huxleyi cells[END_REF], Jakobsen andStrom (2004), Klein Breteler et al. (1999), [START_REF] Klein | Digestion of chlorophylls and carotenoids by the marine protozoan Oxyrrhis marina studied by h.p.l.c. analysis of algal pigments[END_REF], [START_REF] Oosterhuis | Release of the enzyme chitobiase by the copepod Temora longicornis:characteristics and potential tool for estimating crustacean biomass production in the sea[END_REF] Saccharomyces exiguus 2 Droop (1953), Droop (1959) Stoeckeria algicida 1 Jeong et al. (2007) Synechocystis sp. 1 [START_REF] Hammer | The Effect of Electrostatic Charge of Food Particles on Capture Efficiency by Oxyrrhis marina Dujardin (Dinoflagellate)[END_REF] Tetraselmis suecica 1 [START_REF] Hansen | Grazing in the heterotrophic dinoflagellate Oxyrrhis marina: size selectivity and preference for calcified Emiliania huxleyi cells[END_REF] Yeast 5 [START_REF] Cachon | Ultrastructure of the flagellar apparatus of Oxyrrhis marina[END_REF], [START_REF] Cosson | Swimming behaviour of the unicellular biflagellate Oxyrrhis marina: in vivo and in vitro movement of the two flagella[END_REF], [START_REF] Cosson | Inhibition of flagellar beat frequency by a new anti-β-tubulin antibody[END_REF]), Gognon et al. (1994), Godart and Hoitorel (1992) Yeast extract 1

  issue, describe the broad trends in the distribution of O. marina in these samples), and our subsequent sampling database provides a number of useful guidelines for the collection of O. marina.First, the rate of recovery of O. marina from intertidal environments is remarkably consistent; across our whole study, O. marina is consistently recovered from ~50% of

  ) suggested that O. marina thrives between 4 and 130 (PSU) and indicated optimum growth at 16 PSU for the Finnish strain CCAP 1133/5. He also demonstrated an affect of acclimation on cell viability following salinity shifts: cells acclimated to 8 PSU suffered high mortality when transferred to high salinities (32-64 PSU), but cells acclimated to 64 PSU remained viable when transferred to salinities as low as 8 PSU.Lowe et al. (2005) demonstrated salinity tolerances between 5-55 PSU but showed that both tolerance and maximum growth varied between different strains and isolates.Lowe et al. (2005) also indicated two salinity responses, which appeared to correlate with habitat: intertidal strains grew best at relatively high salinities (i.e. >30 PSU); open-water strains grew best at low salinities (i.e. <30 PSU).

  described a fully-soluble derived medium and highlighted the unusual nutritional mode of O. marina. While Droop and Co-workers provided an extensive understanding of the nutritional requirements of O. marina, the physiological mechanisms underlying its somewhat exceptional nutritional flexibility remain unresolved. Investigating such mechanisms is likely to provide novel future research directions.

  survival. Clearly, in a research context, the ability to culture O. marina cells axenically is potentially useful in generating material for genetic analyses. In our laboratory, Droop's axenic medium supports growth of a range of genetically diverse O. marina isolates, suggesting that most 'variants' of O. marina can grown axenically on a soluble nutrient diet.

  protists represent a relatively understudied component of total microbial diversity[START_REF] Caron | Protists are microbes too: a perspective[END_REF]; as a result detailed genetic, physiological and behavioural study of an increasingly broad range of model protist taxa represents an important focus of contemporary microbiological research. This review emphasises why O. marina has proved a useful model protist: it is abundant, relatively simple to isolate from the environment and straightforward to maintain in the laboratory. Perhaps more importantly, this practicality means that O.

Fig. 1 .

 1 FIGURE LEGENDS

Fig. 2 .Fig. 3 .

 23 Fig. 2. Light micrographs of Oxyrrhis marina. a) and b) acidified Lugol's iodine fixed (2%)

Fig. 4 .

 4 Fig. 4. A summary of prey species/food sources demonstrated to allow growth of Oxyrrhis

  Table.1. Components of a medium for the axenic culturing of Oxyrrhis marina. The medium is a modification of that presented byDroop (1959b).

	Component	Stock	Final (~1L)
		solutions	medium
	GF/C filtered autoclaved seawater (32 PSU)	-	750 ml
	Amino acid/Sodium acetate solution (pH 7.5), containing:	300 ml	22.5 ml
	• Glycylglycine hydrochloride (e.g. Sigma G1127) • L-valine (e.g. Sigma 94619) • L-proline (e.g. Sigma P5607) • Sodium acetate F o r	5 g 2.5 g 0.4 g 20 g
	F/2 medium without silicate (e.g. Sigma G0154) P	-	20 ml
	Cholesterol solution (8mg/ml), containing: • water soluble cholesterol (e.g. Sigma C4951) e e r	5 ml 40 mg	5 ml
	Coenzyme Q 10 solution (100 µg/ml), containing: • 2 mg coenzyme Q 10 in 1 mL ethyl acetate added to 19 ml 0.2% glycerol trioleate in absolute ethanol* 1× Leibovitz L-15 medium (e.g. Gibco 21083) + 2.4% (w/v) NaCl i 20 ml -w e v e R 162x126mm (600 x 600 DPI)	200 µl 200 ml

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ACKNOWLEDGEMENTS

The authors would like to thank Zhou Yang for providing the temperature vs growth rate responses for O. marina isolates (Fig. 3). Michael Steinke provided constructive comments on the manuscript and a large number of friends, family and colleagues, too numerous to mention, assisted with sample collection. We would also like to thank two anonymous reviewers for their comments on a previous version of the manuscript.

FUNDING

This work was, in part, supported by a UK NERC grant (NE/F005237/1) awarded to PCW, CDL, and DJSM, and UK NERC grants NE/C519438/1 and NE/G010374/1 awarded to ECR and Dr E. Dudley.

F o r P e e r R e v i e w

1 Supplementary Table. 1. A summary of prey species/food sources demonstrated to allow growth of Oxyrrhis marina in laboratory cultures, including supporting literature citations. Data are synthesised from 72 peer-reviewed manuscripts published between 1953 and 2008.

Prey item/food type

Literature reports

Reporting Articles

Amphidinium carterae 4

Jeong et al. (2001), Jeong et al. (2004), Jeong et al. (2007), [START_REF] Jeong | Feeding by the Heterotrophic Dinoflagellate Oxyrrhis marirta on the Red-Tide Raphidophyte Heterosigma akashiwo: a Potential Biological Method to Control Red Tides Using Mass-Cultured Grazers[END_REF] Artificial medium 2 Droop (1953), Gao and Li (1986) Artificial medium (lemon factor) 1 Droop (1959a) Artificial medium (OX 7) 3 Droop and Pennock (1971), Slamovits and Keeling (2008), Slamovits et al. (2007) Artificial medium (ubiquinone) 1 Droop and Doyle (1966) Artificial medium (Provasoli seawater) Cryptomonas sp. 1 [START_REF] Strom | Planktonic grazers are a potentially important source of marine dissolved organic carbon[END_REF] Diatoms (undefined) 1 [START_REF] Roberts | The flagellar apparatus of Oxyrrhis marina (Pyrrophyta)[END_REF] Dunaliella primolecta 5

Flynn and Fielder (1989), [START_REF] Flynn | Prey selection and rejection by a microflagellate; implications for the study and operation of microbial food webs[END_REF], [START_REF] Martel | Morphological controls on cannibalism in a planktonic marine phagotroph[END_REF], Opik and Flynn (1989) Goniomonas amphinema 1 Martin-Cereceda et al. (2008) HESNW medium 1 Saldarriaga et al. (2003) Heterocapsa rotundata 1 Jakobsen and Strom (2004) Heterosigma akashiwo 1 [START_REF] Jeong | Feeding by the Heterotrophic Dinoflagellate Oxyrrhis marirta on the Red-Tide Raphidophyte Heterosigma akashiwo: a Potential Biological Method to Control Red Tides Using Mass-Cultured Grazers[END_REF] Isochrysis galbana 19 [START_REF] Archer | Microbial dynamics in coastal waters of East Antarctica: herbivory by heterotrophic dinoflagellates[END_REF], [START_REF] Archer | A dilution approach to quantify the production of dissolved dimethylsulphoniopropionate and dimethyl sulphide due to microzooplankton herbivory[END_REF], [START_REF] Barlow | Grazing and degradation of algal pigments by marine protozoan Oxyrrhis marina[END_REF], Buskey et al. (1998), [START_REF] Davidson | Predator-prey interactions between Isochrysis galbana and Oxyrrhis marina . HI . Mathematical modelling of predation and nutrient regeneration[END_REF], Flynn and Davidson (1993), Flynn andDavidson (1993a), Flynn et al. (1996), [START_REF] Goldman | Dynamics of herbivorous grazing by the heterotrophic dinoflagellate Oxyrrhis marina[END_REF], [START_REF] Hansen | Grazing in the heterotrophic dinoflagellate Oxyrrhis marina: size selectivity and preference for calcified Emiliania huxleyi cells[END_REF], [START_REF] Hansen | Phaeocystis blooming enhanced by copepod predation on protozoa: evidence from incubation experiments[END_REF], Kimmance et al. (2006), [START_REF] Martel | Prey location, recognition and ingestion by the phagotrophic marine dinoflagellate Oxyrrhis marina[END_REF], [START_REF] Martel | Morphological controls on cannibalism in a planktonic marine phagotroph[END_REF], Menden-Deuer and Grunbaum ( 2006), [START_REF] Mitra | Predator-prey interactions: is 'ecological stoichiometry' sufficient when good food goes bad?[END_REF], [START_REF] Oosterhuis | Release of the enzyme chitobiase by the copepod Temora longicornis:characteristics and potential tool for estimating crustacean biomass production in the sea[END_REF], [START_REF] Pelegri | Use of high temperature catalytic oxidation (HTCO) to measure carbon content of microorganisms[END_REF], [START_REF] Tang | Trophic modification of food quality by heterotrophic protists: species-specific effects on copepod egg production and egg hatching[END_REF] Karlodinium veneficum 1 [START_REF] Adolf | Karlotoxin mediates grazing by Oxyrrhis marina on strains of Karlodinium veneficum[END_REF] Luciella masanensis 1 Jeong et al. (2007) Micromonas pusilla 2 [START_REF] Flynn | Prey selection and rejection by a microflagellate; implications for the study and operation of microbial food webs[END_REF], [START_REF] Hansen | Grazing in the heterotrophic dinoflagellate Oxyrrhis marina: size selectivity and preference for calcified Emiliania huxleyi cells[END_REF] Nannochloris atomus 1 [START_REF] Davidson | The role of prey nutritional status in governing protozoan nitrogen regeneration efficiency[END_REF] Nannochloropsis sp. 1 [START_REF] Hansen | Grazing in the heterotrophic dinoflagellate Oxyrrhis marina: size selectivity and preference for calcified Emiliania huxleyi cells[END_REF] Nanochloropsis oculata 1 [START_REF] Pond | Monitoring microbial predator-prey interactions: an experimental study using fatty acid biomarker and compound-specific stable isotope techniques[END_REF] Natural bacteria 2 [START_REF] Hammer | The Effect of Electrostatic Charge of Food Particles on Capture Efficiency by Oxyrrhis marina Dujardin (Dinoflagellate)[END_REF], [START_REF] Stevens | Incorporation of bacterial fatty acids and changes in a wax ester-based omnivory index during a long-term incubation experiment with Calanus glacialis Jaschnov[END_REF] Navicula sp. 1 [START_REF] Clarke | The occurrence of body scales in Oxyrrhis marina Dujardin[END_REF] Nitzschia sp. 1 [START_REF] Clarke | The occurrence of body scales in Oxyrrhis marina Dujardin[END_REF] Pavlova lutheri 1 [START_REF] Davidson | The role of prey nutritional status in governing protozoan nitrogen regeneration efficiency[END_REF] Perkinsus marinus 1 [START_REF] Lund | Mechanism(s) of long chain n-3 essential fatty acid production in two species of heterotrophic protists: Oxyrrhis marina and Gyrodinium dominans[END_REF] Pfiesteria piscicida 1 Jeong et al. (2007) Phaeocystis cf. globosa 1 [START_REF] Hansen | Phaeocystis blooming enhanced by copepod predation on protozoa: evidence from incubation experiments[END_REF] Phaeodactylum tricornutum 3 [START_REF] Archer | Microbial dynamics in coastal waters of East Antarctica: herbivory by heterotrophic dinoflagellates[END_REF], [START_REF] Barlow | Grazing and degradation of algal pigments by marine protozoan Oxyrrhis marina[END_REF], [START_REF] Goldman | Dynamics of herbivorous grazing by the heterotrophic dinoflagellate Oxyrrhis marina[END_REF] Prorocentrum minimum 1 [START_REF] Jeong | Interactions among the toxic dinoflagellate Amphidinium carterae, the heterotrophic dinoflagellate Oxyrrhis marina, and the calanoid copepods Acartia spp[END_REF]


Mickael Fabregue

Sandra Bringay
email: bringay@lirmm.fr

Pascal Poncelet

Maguelonne Teisseire

Béatrice Orsetti

Mining microarray data to predict the histological grade of a Breast Cancer

Keywords: Sequential patterns, Microarrays analysis, Breast cancer, Translational Bioinformatics

Background: The aim of this study was to develop an original method to extract sets of relevant molecular biomarkers (gene sequences) that can be used for class prediction and can be included as prognostic and predictive tools. Materials and Methods: The method is based on sequential patterns used as features for class prediction. We applied it to classify breast cancer tumors according to their histological grade. Results: We obtained very good recall and precision for grade 1 and 3 tumors, but, like other authors, our results were less satisfactory for grade 2 tumors. Conclusions:

We demonstrated the interest of sequential patterns for class prediction of microarrays and we now have the material to use them for prognostic and predictive applications.

Introduction

Breast cancer is a major public health issue today. According to the breastcancer.org1 , with 192,370 new cases in 2009 in the U.S., breast cancer is the most frequently diagnosed malignancy and the main cause of cancer death in women. One out of eight women will develop breast cancer during her lifetime. New treatments are continually being developed to target specific types of cancer and to reduce potentially adverse effects (cardiac dysfunction, premature menopause, etc.). However, despite early detection and new treatments, up to 50% of the women will develop distant metastases, which are unfortunately incurable today. The three major challenges associated with breast cancer are: [START_REF] Simon | Experimental design of DNA microarray experiments[END_REF] How to diagnose breast cancer as early as possible through population screening and to identify the type of tumor detected? [START_REF] Alon | Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays[END_REF] How to predict the response of a patient to a given treatment according to classes of individuals? (3) How to choose the best therapy for a given subject with an accurate prognosis including her chances of remission, by deducing from the usual course of the disease its future development and its outcome? DNA microarrays are powerful tools to draw a genetic portrait of a biological sample (e.g., a tumor sample) by comparing gene expression in different tissues, cells, and conditions, and providing information on the relative levels of expression of thousands of genes among samples. These technologies carry with them the hope of bringing new insights to cancer biology and improving current tools for cancer management. Simon and Dobbin [START_REF] Simon | Experimental design of DNA microarray experiments[END_REF] describe three ways of using DNA microarrays:

• Class comparison consists in identifying variations (e.g., in the expression of the genes) among n classes. It can be used to compare normal tissues and tumors [START_REF] Alon | Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays[END_REF], and tumors that respond to therapy and those that do not [START_REF] Rosenwald | The use of molecular profiling to predict survival after chemotherapy for diffuse large-B-cell Lymphoma[END_REF], or to distinguish various subtypes of a tumor [START_REF] Dougherty | Small sample issues for microarray-based classification[END_REF][START_REF] Sotiriou | Breast cancer classification and prognosis based on gene expression profiles from a population-based study[END_REF].

Class comparison enables identification of the critical role of certain genes by establishing the molecular identity of a class, like a bar code. This code can then be used for class prediction.

• Class discovery consists in discovering new subgroups in a population (e.g., subtypes of a tumor) based on the molecular profile. For example, Sotiriou et al. [START_REF] Sotiriou | Breast cancer classification and prognosis based on gene expression profiles from a population-based study[END_REF] describe subtypes of breast cancer.

• Class prediction uses the results of the previous process to assign a new specimen (a new microarray) to a known class, e.g. to a subtype of a tumor [START_REF] Van De Vijver | A gene-expression signature as a predictor of survival in breast cancer[END_REF]. If the classifier is confident, the result can be used by medical experts to make clinical decisions (e.g., for population screening) to predict the effects of a treatment for a patient or for prognoses.

The objective of this study was to develop an original method to extract sets of relevant molecular biomarkers (gene sequences) that can be used for class prediction and as a prognostic and predictive tool. Molecular biomarkers are generated from analyses of DNA microarrays and are based on a particular data mining technique: Sequential pattern discovery. In [START_REF] Paola | Mining Discriminant Sequential Patterns for Aging Brain[END_REF], we described an efficient algorithm to extract these frequent patterns of correlated genes ordered according to their level of expression. An example of such a pattern is < (17aag o vca d n)(tgz a dip u p, rett d n) >,80%Gr1, 40%Gr2 meaning that "For 80% of Grade 1 tumors, and 40% of Grade 2 tumors, the level of expression of gene 17aag o vca d n is lower than that of tgz a dip u p and rett d n, whose levels of expression are very close". Sequential patterns have already been used successfully for text categorization. In this paper, we investigate the relevance of such patterns for tumor classification. The complexity of the data and the interdisciplinary context make this task extremely challenging.

Our contribution is described in terms of methodology, biological findings and medical implications.

After briefly presenting the state of the art (section 2), we describe the complete methodology in detail in the material and methods (section 3). We apply this methodology to the study of breast cancer (section 4). To conclude, we discuss how this methodology can be generalized (section 5) according to the kind of data and the data mining approach.

Background

Due to the amount of data available, processing DNA microarrays in a way that makes biomedical sense is still a major issue. Statistical methods and data mining techniques play a key role in discovering previously unknown knowledge. However, their implementation in this context is difficult because the number of measurement points (gene expression levels) is much higher than the number of samples, which results in the well-known problem of the curse of dimensionality, also called the high feature-to-sample ratio [START_REF] Dougherty | Small sample issues for microarray-based classification[END_REF]. Moreover, the correlation structure of the expressions is unknown (gene co-expressions) and the presence of noise is a serious problem. For all these reasons, classification based on microarray data is quite different from previous classifications and traditional methods are not successful [START_REF] Zupan | Machine Learning for Survival Analysis: A Case Study on Recurrence of Prostate Cancer[END_REF].

Most studies are based on the search for differentially expressed genes, particularly disease-specific genes. These methods work like a filter and reduce the size of the group of genes in the experiment to a smaller one, which can be more easily investigated. Most widely used methods use univariate procedures often combined with adjustment of P-values or a similar concept [START_REF] Dudoit | Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments[END_REF][START_REF] Tusher | Significance analysis of microarrays applied to the ionizing radiation response[END_REF]. SAM [START_REF] Tusher | Significance analysis of microarrays applied to the ionizing radiation response[END_REF] or CyberT [START_REF] Baldi | A Bayesian framework for the analysis of microarray expression data: regularized t-test and statistical inferences of gene changes[END_REF] are well-known programs based on such techniques. Unlike multivariate approaches such as ANOVA, these methods do not take into account the multidimensional structure of the data [START_REF] Nueda | Discovering gene expression patterns in time course microarray experiments by ANOVA-SCA[END_REF].

We could also cite other approaches based on combinations of various artificial intelligence techniques [START_REF] Li | Gene selection for sample classification based on gene expression data: study of sensitivity to choice of parameters of the GA/KNN method[END_REF][START_REF] Paola | Mining Discriminant Sequential Patterns for Aging Brain[END_REF]. However, several authors [START_REF] Choe | Preferred analysis methods for Affymetrix GeneChips revealed by a wholly defined control dataset[END_REF][START_REF] Dudoit | Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments[END_REF] have compared most of these methods and shown that they do not necessarily detect the same subset of differentially expressed genes. Nevertheless, the above-mentioned methods do help rank the genes for the development of biomarkers that can be used for class discovery. Differentially expressed genes are features used to discriminate subgroups of specimens. Many diseases are heterogeneous and characterized by the presence of several subgroups. This is the case of breast cancer [START_REF] Sorlie | Gene expression patterns breast carcinomas distinguish tumor subclasses with clinical implications[END_REF]. The discovery of associations between prognostic information and responses to therapy and the molecular signatures that characterize subgroups has greatly facilitated the development of treatments tailored to specific subgroups. To discover the subgroups concerned, we focus on the case where the experiments monitor the gene expression of different tissue samples, and the aim is to find a structure in this collection of unlabeled data to associate with a category, describing, for example, a subgroup of tumors. Several authors [START_REF] Peng | A novel ensemble machine learning for robust microarray data classification[END_REF][START_REF] Sorlie | Gene expression patterns breast carcinomas distinguish tumor subclasses with clinical implications[END_REF][START_REF] Sotiriou | Breast cancer classification and prognosis based on gene expression profiles from a population-based study[END_REF] have published such lists concerning breast cancer.

Once the subgroups are defined, it is possible to associate a new microarray with a class with class prediction by comparing a new specimen to features describing the subgroups. Several authors [START_REF] Alizadeh | Distinct types of diffuse large b-cell lymphoma identified by gene expression profiling[END_REF][START_REF] Brown | Knowledge-based analysis of microarray gene expression data by using support vector machines[END_REF][START_REF] Peng | A novel ensemble machine learning for robust microarray data classification[END_REF][START_REF] Wong | Two-stage classification methods for microarray data[END_REF] have proposed successful methods but it is still too difficult to use them to improve breast cancer prognosis or prediction [START_REF] Pusztai | Chips to bedside: incorporation of microarray data into clinical practice[END_REF]. The pitfalls have been emphasized by many authors [START_REF] Michiels | Prediction of cancer outcome with microarrays: a multiple random validation strategy[END_REF][START_REF] Simon | Experimental design of DNA microarray experiments[END_REF], these include the risk of over-fitting due to the high feature-to-sample ratio and the lack of validation due to the absence of independent datasets or the incorrect use of cross-validation techniques. Although the number of measured genes is in the thousands, it is assumed that only a few genes determine the type of a tissue. More recent studies focus on finding such groups of genes.

In this paper, we do not try to find the minimum subsets of genes but look for gene sequences that we can use as features for the prediction of different classes.

Material and Methods

The class prediction system involves two steps: Microarray G1 G2 G3 G4 G5 M1 6.76 6.65 6.65 9.65 6.75

Associated < (G2G3G5)(G1)(G4) > sequences < (G2G3)(G5G1)(G4) >
Table 1: Gene expressions for microarray M1 and two associated data sequences with a minimal gap of 0.1

Sequence preprocessing module:

For each microarray, we have a list of genes associated with an expression value (see Table 1).

The aim of this step is to build sequences by ordering the genes according to their value. In classical database vocabulary, the genes are called items. An itemset it i is a non-ordered group of genes with similar expression. By considering the gaps between the expression of the genes (see Table 1), G2

and G3 are grouped in the same itemset because they have the same expression, but considering a minimal gap equal to 0.1, G5 can be either grouped in it 1 = (G2G3G5) or in it 2 = (G1G5). A sequence S =< it a it b ...it p > is a non-empty and ordered list of p itemsets, i.e. groups of genes ordered according to their expression. From a microarray, we generate as many sequences as there are possible itemsets. Table 2 gives associated data sequences with a minimal gap of 0.1.

Feature selection module:

Table 2 gives an example of data used as input in the feature selection module. The aim of this step is to build sequential patterns [START_REF] Agrawal | Fast algorithms for mining association rules[END_REF], in our case frequent sequences of genes, to characterize a class. A pattern is supported by a microarray if the pattern is included in one or more sequences associated with a microarray. For example (see Table 2), the pattern P =< (G2)(G5) > is included in one of the two M 1 data sequences. So, P is supported by the microarray class 1 . The support of a pattern P in a class class i , denoted by support class i (P ), is defined as the percentage of microarrays Microarray Class Associated genes sequences. that support P in that class i . For example, support 1 (P ) = 3/3 and support 2 (P ) = 1/2. To obtain the most frequent patterns, a minimum support is provided and the patterns extracted must have a support greater this threshold, called the minimum support. For instance, if the minimum support is equal to 2/3, P is frequent in class 1 but not in class 2 . These definitions were given in a previous work [START_REF] Dougherty | Small sample issues for microarray-based classification[END_REF], and an efficient algorithm was developed. In this paper, we have adapted the PrefixSpan algorithm [START_REF] Pei | PrefixSpan: Mining Sequential Patterns Efficiently by Prefix-Projected Pattern Growth[END_REF] to take into account n sequences associated with a microarray. [START_REF] Duong | Sequence data mining[END_REF] have shown that Prefixspan is pseudo-polynomial. The complexity is O((2N ) ∧ L) where N is the number of items and L is the maximum length of the initial gene sequences of the microarrays.

M1 1 < (G2G3G5)(G1)(G4) > < (G2G3)(G5G1)(G4) > M2 1 < (G1)(G4)(G2)(G3)(G5) > M5 1 < (G2 G5)(G4)(G3)(G1) > < (G2)(G5G4)(G3)(G1) > M3 2 < (G1)(G4)(G5)(G2)(G3)) > M4 2 < (G1)(G2)(G3)(G4)(G5) >
For class prediction, we only look for relevant patterns and not for all patterns. We rank the patterns to keep only the k best patterns for each class according to a measure based on the support value. For each pattern, the ranking measure is the difference between their two highest supports.

For example (see Table 3), the gap between the two highest supports for pattern P 1 is 0. Table 3: Gaps obtained for two patterns for 3 classes. For each pattern, support has been computed for each class. For a particular, the best gap is equal to the difference between the two highest supports. In this example P2

"is better" than P1 because P2 has the highest best gap.

P 2, 0.5. Consequently, pattern P 2 has a better rank than pattern P 1. The interest of these patterns is that they can be used to distinguish classes but they also enable to take into account additional information with respect to differentially expressed genes, i.e. the order of expression of correlated gene groups.

Classification module:

The objective is to assign S =< (G1)(G2G3)(G4)(G5G6)(G7)(G8)(G9)(G10G11) > an unlabelled sequence to a class (a category of tumor). We compare S to n% of the ranking patterns by class.

Consider the patterns P 1, P 2, P 3 (see Table 4), with P 1, P 3 for class2, and P 2 for class3. When S contains a pattern, the score of S for the class associated with the pattern is increased by 1. Table 5 gives the score of S for each class. As the highest score is for class2, S is assigned to class2.

To evaluate the classification, we measure the precision and the recall for each class. Precision is the number of sequences correctly assigned to a class divided by the total number of sequences assigned to this class (correctly or not). The recall is the number of sequences correctly assigned to a class, divided by the number of sequences of real data belonging to this class. Table 6 gives an example of such a calculation. An F-measure combines Precision and Recall according to Formula 1:

Patterns Class 1 Class 2 Class 3

P 1 =< (G1)(G2G3)(G4) > 0.2 0.8 0.1 P 2 =< (G5G6)(G7)(G8) > 0.1 0.0 0.9 P 3 =< (G9)(G10G11) > 0.3 0.7 0.1
S =< (G1)(G2G3)(G4)(G5G6)(G7)(G8)(G9)(G10G11) > 0 2 1

Number of sequences

Class Associated with the class Correctly labeled Labelled .

F = 2 * precision * recall precision + recall (1)

Experiments

Datasets and objectives: We examined the following microarray datasets: a dataset provided by the IRCM which is not public, and datasets available online from Gene Expression Omnibus 2 KJX64-KJ125 (GSE2990), TAM (GSE6532), and TBG2 (GSE7390), focusing on a total of 624 human Affymetrix microarrays HG 133. All these microarrays share 22000 probesets 3 . To start the study, we focused on a subset of this list, the 128 genes identified by [START_REF] Sotiriou | Breast cancer classification and prognosis based on gene expression profiles from a population-based study[END_REF] for breast cancer. Below, we illustrate the power of classification based on sequential patterns in the case of breast cancer through one question: how to classify a new microarray according to its histological grade [START_REF] Elston | The value of histological grade in breast cancer: experience from a large study with long-term follow-up[END_REF][START_REF] Scarff | histological classification of tumours[END_REF]? This grade is a well-known variable with three values. It is used in clinical studies for its high prognostic potential in breast cancer. For example, patients with a grade 1 tumor have better survival rates than those with a grade 3 tumor. The distribution of the microarrays is 162 for grade 1, 274 for 2 and 185 for 3. 3 Even though it is misusing the language, we use the term gene for probeset.

Extraction of sequential patterns:

The extraction parameters are defined experimentally. As shown in Figure 1, in this type of data, it is difficult to extract patterns with a minimum support in a reasonable timeframe (we only keep patterns with a support greater than a given threshold named minimum support). We do not look for all patterns but only for a subset of patterns enabling efficient classification. For rapid extraction, we split the gene base into few groups and extract patterns from each. We experimentally vary the number of genes and the support. We observed that the most accurate approach is to form groups of 42 genes that can be extracted in 350 seconds with a miniuml support of 0.4. Classification: We used a cross-validation process to assess how the results of our classifier are generalized to an independent dataset. One round of cross-validation involves distributing the data into complementary subsets, building the classifier on the training set, and validating the analysis on the validation set. According to the results deduced from Figure 2, we extracted sequential patterns on 80 specimens (38% of the total base) and validated the classifier on the remaining specimens (62%).

To reduce variability, multiple rounds (50) were performed using different distributions. We used the 100 best sequential patterns for each grade.

Table 7 shows the evaluation of the method for the three grades. The method remains valid for more than three classes. We obtained optimistic results for grade 1 and 3 (Recall) and bad results for grade 2. These results are consistent with [START_REF] Sotiriou | Breast cancer classification and prognosis based on gene expression profiles from a population-based study[END_REF] who found that breast cancers of grades 1 and 3 had distinct gene expression profiles that appear in the patterns, but that grade 2 had heterogeneous gene expression profiles that are not captured by the patterns. In most cases, the specimens are wrongly classified in grade 1 or 3 (Precision). The line 4 of Table 7 corresponds to the genes used in the patterns that describe a grade. The last line gives the union between the genes involved in each grade. It should be noted that the genes are not the same for each grade. The genes can be ranked according to their efficiency for class prediction thank to the number of patterns in which they appear and all genes used to construct the pattern can be reduced considering the best genes. By considering only grades 1 and 3, and the 3 grades (Table 8), we compared our classifier with those of Weka software that refer to the data mining community. We calculated the recall, the precision and the F-measure for each group of classifiers. Considering only grade 1 and 3 or only grade 3, we obtained the higher F-measure with the IRCM dataset in all cases. The results were least satisfactory when considering the combination of IRCM and online datasets or online datasets alone.

We can make two assumptions: 1) the online datasets are heterogeneous and it is more difficult to obtain relevant sequential patterns: the microarrays were obtained from patients undergoing different treatments, with different types of tumor and many others parameters that affect gene expression.

2) Our classifier is more effective for an imbalanced dataset. Unsatisfactory results were obtained for grade 2 tumors (table 7) with all the datasets, but optimist results with the IRCM dataset.

From a list of patterns, we can effectively classify tumors into grades. Unlike a list of differentially expressed genes specific to a class, the patterns can be used to compare different classes and thus provide answers to different questions concerning prognosis. We can take into account all the DNA microarrays available online and the associated contextual information to produce a bar code (list of

Step 1 -

 1 Building the classifier: (1) The sequence preprocessing module transforms the raw data into gene sequences; (2) The feature selection module extracts sequential patterns, which have a close relationship with a given type of class; Step 2-Evaluation of the classifier: The classification module makes decisions concerning categories of testing samples and examines whether the classification results are confident or not. Details of the methods used in each module are described in Sections 3.1, 3.2 and 3.3.

Figure 1 :

 1 Figure 1: Extraction time vs. minimal support

Figure 2 :

 2 Figure 2: Stability of the generation of the patterns

Table 2 :

 2 Gene sequences for 5 microarrays and 2 classes. The microarrays M1, M2 and M5 are associated with the class 1 and M3 and M4 are associated with the class 2. According to a minimal gap, 2 sequences are associated with the microarray M1 and M5 and 1 sequence is associated with the microarrays M2, M3 and M4.

Table 4 :

 4 Distribution of the sequential patterns in 3 classes. As P1 and P3 have the highest support in Class 2, they are associated with Class 2. P2 is associated with Class 3.

	Sequence

Table 5 :

 5 Scores by class associated with sequence S. According to the distribution in Table4, the sequence S is included in 0 pattern of class 1, in 2 patterns of class 2 and in 1 pattern of class 3.

Table 6 :

 6 Example of results obtained after cross validation.

	Precision=15/20, Recall=15/18 and F-measure=

Table 7 :

 7 Evaluation of the classifier per grade. For a total of 104 genes (68 involved in sequences associated with Class 1, 57 with Class 2 and 55 with Class 3), we obtain various measures of Recall, Precision and F-measure by class.

		Grade 1 Grade 2 Grade 3
	Recall	.81	.15	.86
	Precision	.39	.76	.54
	F-Measure	.53	.25	.66
	Involved genes	68	57	55
	Total genes		104

Table 8 :

 8 Classifier evaluation. Family of classifiers available in Weka are compared to our method in the last line entitled SP in term of Recal, Precision and F-measure. We vary the number of class (Grade 1 and 3 / Grade 1, 2 and 3) and the datasets (IRCM, IRCM and online datasets and online datasets alone). The highest F-measure scores are in bold in this table.

						Grade 1 and 3				Grade 1, 2 and 3
	Classifier		IRCM		IRCM and online datasets	Online datasets		IRCM
		R	P	F	R	P	F	R	P	F	R	P	F
	Rules (9)	0.954	0.967	0.959	0.922	0.922	0.922	0.924	0.906	0.915	0.715	0.706	0.710
	Bayes (8)	0.921	0.932	0.926	0.819	0.826	0.822	0.920	0.918	0.819	0.702	0.716	0.708
	Functions (5)	0.955	0.970	0.962	0.902	0.901	0.902	0.917	0.918	0.917	0.760	0.802	0.779
	Lazy (4)	0.909	0.939	0.923	0.922	0.931	0.926	0.937	0.943	0.940	0.727	0.721	0.724
	Misc (3)	0.934	0.942	0.937	0.937	0.934	0.936	0.932	0.936	0.934	0.736	0.714	0.724
	Tree (12)	0.928	0.944	0.936	0.943	0.944	0.944	0.938	0.943	0.940	0.765	0.770	0.767
	SP	0.962	0.974	0.968	0.896	0.910	0.903	0.891	0.880	0.885	0.769	0.797	0.782

http://www.breastcancer.org/

Author-produced version of the article published in Journal of Biomedical Informatics, 2011, 44 patterns) from a limited set of genes (one hundred). A category could be: a grade 2 tumor, between 2 and 3 cm, treated with hormones, etc. Once a patient is classified in a category, we can use the information about the future of the patient already assigned to a class to predict her resistance to the various therapies or to make a prognosis for each choice of therapy.

Conclusions and Prospects

In this paper, we focus on the classification of DNA microarrays based on sequential patterns.

Our contribution is two-fold: (i) we have developed a classification technique based on sequential patterns and not on differentially expressed genes, which is the case of most of the methods cited in the literature; (ii) we checked it experimentally to verify the interest of these features for the classification of tumors according to their histological grade. We have shown that the method is effective at highlighting biological differences between grade 1 and 3 tumors and is better than other classifiers when the datasets are imbalanced. Like the other methods, the classification is not efficient for grade 2 tumors. We hope to improve these results by using another form of distribution described by [START_REF] Sotiriou | Breast cancer classification and prognosis based on gene expression profiles from a population-based study[END_REF]. We try now to improve the patterns extraction module to manage more genes. We can also go a step further and use this technique for prediction and prognosis.

Conflict of Interest

None declared.

Author-produced version of the article published in Journal of Biomedical Informatics, 2011, 44, S12-S16. The original publication is available at www.elsevier.com/locate/yjbin DOI :10.1016/j.jbi.2011.03.002


Notes on the first chapter of The Continuum:

Intension, extension and arithmetism. BERNARD

Abstract :

In The Continuum, Hermann Weyl gives new bases to the notions of set and function. With them, he constructs mathematics close to physics and solves the continuum problem. Those new notions are so unusual with respect to Set Theory that they are often misunderstood.

We propose to explain the meaning of Weyl's reform of those notions. We first make a synthesis of his main epistemological thesis, and then propose a comparative approach to stress the distance between the mathematical and logical principles of The Continuum and those of Set Theory. Our discussion will be centred on the distinction between intension and extension, and on the place Weyl gives to natural numbers for the foundations of analysis.


Julien Bernard
email: ju_bernard@yahoo.fr

From the Hole Argument (A.Einstein) to the Ball of Clay Argument (H. Weyl)

The hole argument is a story invented by Albert Einstein to set out the difficulties he had in reconciling his principle of covariance with the Mach's principle. Some modern presentations insist that the bare differential manifold loses its physical status and is just an expression of the mathematical framework of the new relativistic theory.

In Space-Time-Matter, Hermann Weyl constructed an argument close to the modern hole argument, replacing the hole with a ball of clay. Beside some trivial technical differences, Weyl's argument is original because of the particular concept of mathematics that he inherited from the Gottingen school. In 1918, Hermann Weyl published Space-Time-Matter, one of the first general handbooks on General relativity. Weyl thought with enthusiasm that Albert Einstein's theory is a brilliant confirmation of Bernhard Riemann's epistemological ideas on geometry. That involves a redistribution of the roles of mathematics and physics in the scientific constitution of the space concept. In a short text from Space-Time-Matter, Weyl explains how this redistribution works in a theory like general relativity, that is in a Riemannian space where the metrical coefficients are determined by matter. For his explanation, he uses an argument very close formally to the famous Albert Einstein's Hole argument. But, in Weyl's argument, the hole is replaced by a ball of clay which is modeled by hand. We will call it the "ball of clay argument".

(**********)

We will present two different points of view on the BCA.

Firstly, we will provide a comparison between Einstein's Hole Argument and Weyl's BCA. This comparative interpretation will show some differences in the mathematical and physical content of the arguments. And that will highlight some features of GTR-like theories.

Secondly, we will propose an intrinsic interpretation of the BCA. That is a reading from the point of view of Weyl himself. We will see that the excessive simplifications that we meet in Weyl's expression of Mach's principle can be explained by a difference in the philosophical problems guiding both authors. Beyond its formal analogy with the HA, the aim of the BCA is different. It presents an important dilemma, which could be the key idea in understanding the unity of STM, and therefore, the unity of Weyl's thoughts on the space concept. Albert Einstein struggled with both mathematical and conceptual difficulties during the years 1907-1915, when he was searching for a relativistic theory for gravitation. Einstein wanted his field theory to satisfy two strong hypotheses, namely 1) the total determination of the inertia by the distribution of matter (Mach's principle) and 2) the principle of general relativity. He thought that the latter had to be expressed by a general covariant theory, in the context of a Riemannian metric. There $fore, he was looking for tensorial field equations G ab (x) = T ab (x), where T ab (x) is the stressenergy tensor (representing mass), and G ab (x) is a mathematical function of the metrical tensor g ab (x) and its derivatives. However, for a while, some of his difficulties appeared to suggest that such a general schema couldn't provide a correct expression of Mach's principle.

The hole argument, developed by Einstein, was a didactic way to present his momentary belief in this incompatibility.

(**********)

What Einstein wanted to show, in his hole argument, is that, in every theory of the previous kind, there is a kind of indeterminism, in the sense of a violation of Mach's principle.

In such a theory, we could find, for the same field of stress-energy coefficients T ab (x), two different fields of metrical coefficients g ab (x) and g' ab (x) that both verify the gravitational equations (*). The second field is constructed from the first, simply using the fact that the gravitational equations (*) are covariant, and using the hypothesis of a region of space (the hole) that is void of matter. Einstein concluded first that, if we took these kinds of covariant gravitational equations, we had to introduce into the physical theory some indeterminism-something which was unacceptable for him. Let's focus now on a modern presentation of the argument (we think about the interpretation of three Johns: J.Stachel, J.Earman and J.Norton). In their interpretation of the hole argument, they minimize the importance of Mach's principle, and so they minimize the importance of the hole itself.

For them, what is important to understand is that, before we put any field on, space-time as a purely topological manifold is not already a physical entity. It is just a mathematical frame.

We just have to understand that two solutions differing only by an active diffeomorphism are two mathematical expressions of the same physical situation.

We see that the issue, here, differ from that of the original argument.

(**********) Three notions compose the hole argument: the manifold, the metric and the mass (the stress-energy tensor). The modern presentation insists on the relation between on one side, the bare manifold, and, on the other side, the metrical field and the stress-energy field together. Thus, we focus here on the epistemological problem about the relation between the mathematical framework and the physical entities.

In fact, what Einstein really wanted to compare was, on one hand, the manifold with the stress-energy tensor defined on it, and on the other hand, the metrical tensor. The main problem therefore was to think the relation between two physical realities (mass and metric), an ontological problem about the nature of the relations between the metric and the masses.

To solve this original problem, we have to understand that we still have a mathematical freedom in the way we express the metric on the manifold, even when the values of the stress-energy tensor are given everywhere. 1) He posits that the (differential) space-time manifold is R 4 itself 2) He models the content of space-time (matter and energy) by a single scalar function . 3) He gives Mach's principle in a very simple form. He states that the metric is directly a function of the repartition of matter.

Like in the hole argument, Weyl's argument is developed in three steps. (we change just a little the order inside the argument) We start from a certain repartition of matter (x) with a metric g ν (x). Then, we change the repartition of matter to '(x). Finally, we change the frame of coordinates in such a way that the new repartition of matter is expressed in the new frame of coordinates, like the old repartition of matter was expressed in the first frame of coordinates. (Then, have  at step 1 and then again  at step 3, the same mathematical function). Now, we explore two possibilities for the behavior of the metric.

Possibility a)

If the metric is independent from matter. Then, at step 2, the metric does not change. But, when we change the frame of coordinates, at step 3, we change the coefficients of the metric. Therefore, they differ at the end from the initial coefficients. Weyl interpret this by saying that matter cannot move from one point of Space to another without changing its metrical relations.

Possibility b)

If the metric is dependant from matter. Then, the metric changes at step 2. And when change the frame of coordinates at step 3, then the coefficients come back to their first values. We have the same mathematical functions g ν at the end as at the beginning. Weyl interpret this by saying that matter can move from one point of space to another, without changing its metrical relations. Space is than homogeneous. We have, in one sense, the possibility of a rigid motion.

What is important for Weyl is to show that, even in a Riemannian context, we can think about the possibility of a rigid motion, or of the homogeneity of space. In other words, he wants to show that we can move a body from a point of space to another, without changing its intrinsic metrical relations.

Therefore, Weyl concludes that only the case b) is correct. We have to suppose that the metric is dependant from matter, if we want to save homogeneity of space in a Riemannian context. He states that:

"The simple fact that I can squeeze a ball of modeling clay with my hands into any regular shape totally different from a sphere would seem or reduce Riemann's view to absurdity."

Space-Time-Matter, §12

Indeed, Weyl wanted to illustrate the possibility of a rigid motion in a Riemannian context. But the conclusion of his argument is not the possibility but the necessity of the rigidity of motion. The universe as a whole appears in his argument as a unique rigid body where any motion is impossible, even the simple possibility to change the shape of a ball of clay.

Thus, Weyl's ball of clay paradox is a paradox precisely in the same sense as Zeno's paradoxes. It demonstrates the impossibility of any motion, starting just from a few rational hypothesis.

A new kind of paradox of motion like Zeno's 1) If the inner properties of matter can be entirely determined by fields whose signification need not any metric (like scalar fields 2) And if these inner non-metrical properties of matter entirely determine the metric

Then no motion is possible is the universe (without changing the inner properties of matter).

In the text following our quotation, Weyl tries several ways to solve the paradox. Nevertheless, we think that these solutions are less interesting than the reason why a paradox of motion is implied in Weyl's ball of clay argument, but not in Einstein's hole argument.

Indeed, we have a paradox of motion in Weyl's schema, because of his over simplified formulation of Mach's principle. So, by contrast with Einstein's more subtle schema, it demonstrates that, in order to be compatible with the possibility of motion:

1) Mach's principle has to be expressed in a Local-Dynamic (not a Global-Static) form. We have to take time into account in order to express correctly Mach's principle

2) Mach's principle cannot link a totally non-spatial concept of matter with the metric. Rather, it must link matter, as it is distributed in a current metrical web, with the future distribution of matter. Matter does not determine the metric but the evolution of the metric.

(**********)

Now, we turn to the intrinsic approach to the Ball of Clay argument.

We saw that the Ball of Clay Argument of Weyl has mathematical and physical weaknesses with regards to the hole argument of Einstein, because of excessive simplifications. But, beside this, the difference between these arguments highlights an important change in the philosophical issues of these two authors.

Weyl simplifies the modeling of matter because, like in modern interpretations of the hole argument, his main interest is not the way in which matter can entirely determine the metric. For Weyl, this determination is no longer a problem but an hypothesis.

Instead of this, Weyl's problem is now:

In the context of a Riemannian metrics whose coefficients are determined by matter, can we continue to think about geometry as an a priori mathematical knowledge about a space characterized by its homogeneity?

We see that Hermann Weyl's problem is closer to the modern approach of the hole argument than to Einstein's. But his investigation into the link between mathematics and physics in geometry is greatly influenced by a particular concept of mathematics, which is inherited from the Gottingen school.

(**********)

To save the homogeneity of space in this Riemannian context, in the text of the Ball of Clay Argument, he adopts a radical solution. He excludes the notion of metric from the domain of the mathematical geometry, in the strict sense. The space, as the homogeneous object of geometry, is reduced to the topological (differential) notion of manifold. This idea is closely linked to some idea we can find in several Einstein's texts. We have to wait for the third edition of Space-Time-Matter to read about a more subtle solution to Weyl's problem. This more elaborate solution is supplied by the idea of "Nahegeometrie" (we refer to the works of Erhard Scholz for this notion)

The idea is that only the infinitesimally closed relations are the object of an a priori knowledge, whereas relations at a finite distance need the consideration of matter and so is the object of physics.

To conclude, we have first highlighted some important features of Mach's principle, by a comparative interpretation of the Ball of Clay argument with the hole argument. The, we turned to an intrinsic interpretation of the text of the Ball of Clay Argument. And we saw that it can be considered as the place, in Space-Time-Matter, where Hermann Weyl puts down the problem of the conciliation of Riemannian geometry with the idea of the homogeneity of space. That idea of homogeneity was very important for Hermann Weyl, because he defended some kind of idealism of space. Therefore, the issue presented in the Ball of Clay Argument is the key to have a global understanding of the great geometrical works of this author. This is the birth of the epistemological problem that has guided Hermann Weyl to his Nahegeometrie.

Thank you.

  Les signes (**********) représentent les moments où il faut changer de diapositive Powerpoint)

  and the modern presentation of the hole argument :

  Let's turn now to the ball of clay argument. (**********) Contrary to Einstein and the moderns, Weyl uses excessively simplified hypotheses to develop his argument:

  comes to what we can call properly the "Ball of Clay Paradox".