Manhal Mili

Baptiste Panthu

Anne-Marie Madec

Marie-Agnès Chauvin

Gilles J P Rautureau

Bénédicte Elena-Herrmann

Benedicte Elena-Herrmann
email: benedicte.elena@univ-grenoble-alpes.fr

Benedicte Elena-Herrmann

Fast and Ergonomic Extraction of Adherent Mammalian Cells for NMR-based Metabolomics Studies

Keywords: Metabolomics, NMR, adherent cells, extraction, quenching, metabolic profiles

Cellular metabolomics has become key to elucidate mechanistic aspects in various fields such as cancerology or pharmacology, and is rapidly becoming a standard phenotyping tool accessible to the broad biological community. Acquisition of reliable spectroscopic datasets, such as Nuclear Magnetic Resonance (NMR) spectra, to characterize biological systems depends on the elaboration of robust methods for cellular metabolites extraction. Previous studies have addressed many issues raised by these protocols, however with little pondering on ergonomic and practical aspects of the methods that impact their scalability, reproducibility and hence their suitability to high-throughput studies or their use by non-metabolomics experts. Here, we optimize a fast and ergonomic protocol for extraction of metabolites from adherent mammalian cells for NMR metabolomic studies. The proposed extraction protocol, including cells washing, metabolism quenching and actual extraction of intracellular metabolites was first optimized on HeLa cells. Efficiency of the protocol, in its globality and for the different individual steps, was assessed by NMR quantification of 27 metabolites from cellular extracts.

We show that a single PBS wash provides a seemly compromise between contamination from growth medium and leakage of intracellular metabolites. In HeLa cells, extraction using pure methanol, without cell scraping, recovered higher amount of intracellular metabolites than the reference methanol/water/chloroform method with cell scraping, with yields varying across metabolite classes. Optimized and reference protocols were further tested on eight cell lines of miscellaneous nature, and inter-operator reproducibility was demonstrated. Our results stress the need for tailored extraction protocols and show that fast protocols minimising time-consuming steps, without compromising extraction yields, are suitable for high-throughput metabolomic studies. Extraction with methanol without cell scraping Extraction with methanol and cell harvesting by scraping Extraction with methanol/water and cell harvesting by scraping a) b) Concentration (a.u.) Concentration (a.u.)

INTRODUCTION

Metabolomic approaches can provide extensive and instantaneous metabolic snapshots of ongoing biological processes in living systems. They are complementary to other omics strategies, and frequently used in studies related to human health. A wide range of samples, primarily biofluids, tissue and cells extracts, can be exploited for metabolomics studies. Biofluids are typically used to study metabolic consequences of pathophysiological processes on whole organisms as well as to identify biomarkers [START_REF] Zhang | Recent and potential developments of biofluid analyses in metabolomics[END_REF][START_REF] Giskeødegård | NMR-based metabolomics of biofluids in cancer[END_REF], whereas tissue and cell samples are relevant to investigate mechanistic aspects [START_REF] Zhang | Cell metabolomics[END_REF][START_REF] Rinschen | Identification of bioactive metabolites using activity metabolomics[END_REF][START_REF] Aranibar | NMR-based metabolomics of mammalian cell and tissue cultures[END_REF][START_REF] Lefevre | Metabolic phenotyping of adipose-derived stem cells reveals a unique signature and intrinsic differences between fat pads[END_REF]. Cellular metabolomics represents a cost-efficient and flexible approach, with good control of external variables, that is key to unravel essential aspects of cellular differentiation and proliferation [START_REF] Moussaieff | Glycolysis-Mediated Changes in Acetyl-CoA and Histone Acetylation Control the Early Differentiation of Embryonic Stem Cells[END_REF], carcinogenesis [START_REF] Li | The landscape of cancer cell line metabolism[END_REF][START_REF] Ortmayr | Metabolic profiling of cancer cells reveals genome-wide crosstalk between transcriptional regulators and metabolism[END_REF], or potential drug toxicity mechanisms [START_REF] García-Cañaveras | A metabolomics cell-based approach for anticipating and investigating drug-induced liver injury[END_REF]. While an increasing number of metabolomics studies on human adherent cell lines have been described over the past decade [START_REF] Hayton | Experimental design and reporting standards for metabolomics studies of mammalian cell lines[END_REF], preparation of cell extracts well suited for metabolomics studies still faces technical challenges as compared to the sampling of biofluids. Adequate protocols are not only crucial to ensure optimal quality and reproducibility of the analytical data, but they also govern accuracy of the metabolic portrait obtained for the observed biological system. Most evaluations of metabolite extraction procedures have been so far carried out for subsequent use of mass spectrometry coupled with either gas [START_REF] Kapoore | Influence of washing and quenching in profiling the metabolome of adherent mammalian cells: A case study with the metastatic breast cancer cell line MDA-MB-231[END_REF][START_REF] Dettmer | Metabolite extraction from adherently growing mammalian cells for metabolomics studies: Optimization of harvesting and extraction protocols[END_REF][START_REF] Danielsson | Development and optimization of a metabolomic method for analysis of adherent cell cultures[END_REF][START_REF] Kapoore | Cell line dependence of metabolite leakage in metabolome analyses of adherent normal and cancer cell lines[END_REF][START_REF] Hutschenreuther | Comparison of extraction conditions and normalization approaches for cellular metabolomics of adherent growing cells with GC-MS[END_REF] or liquid chromatography [START_REF] Ser | Extraction parameters for metabolomics from cultured cells[END_REF][START_REF] Lorenz | Reducing time and increasing sensitivity in sample preparation for adherent mammalian cell metabolomics[END_REF][START_REF] García-Cañaveras | Extending metabolome coverage for untargeted metabolite profiling of adherent cultured hepatic cells[END_REF][START_REF] Bi | Optimization of harvesting, extraction, and analytical protocols for UPLC-ESI-MS-based metabolomic analysis of adherent mammalian cancer cells[END_REF][START_REF] Peterson | Optimized Method for Untargeted Metabolomics Analysis of MDA-MB-231 Breast Cancer Cells[END_REF] that result in metabolic detection windows and technical requirements, such as chemical derivatization or efficient protein background removal, well specific of these approaches.

Few protocols have been developed towards Nuclear Magnetic Resonance (NMR)-based metabolomic analysis, and focused on selected steps of the overall extraction procedure [START_REF] Teng | A direct cell quenching method for cell-culture based metabolomics[END_REF][START_REF] Martineau | Strategy for choosing extraction procedures for NMR-based metabolomic analysis of mammalian cells[END_REF][START_REF] Le | A comparison of cell and tissue extraction techniques using high-resolution1H-NMR spectroscopy[END_REF].

Metabolite extraction from adherent cells consists in a series of entwined experimental steps that include washing of the cells to get rid of residue from culture media, quenching to stop metabolic activity, and cell harvesting and extraction of the intracellular metabolome using individual solvents or mixtures.

Previous optimizations of metabolite extraction methods from adherent mammalian cell lines have selectively focused on cell washing [START_REF] Kapoore | Influence of washing and quenching in profiling the metabolome of adherent mammalian cells: A case study with the metastatic breast cancer cell line MDA-MB-231[END_REF][START_REF] Ser | Extraction parameters for metabolomics from cultured cells[END_REF], harvesting [START_REF] Dettmer | Metabolite extraction from adherently growing mammalian cells for metabolomics studies: Optimization of harvesting and extraction protocols[END_REF][START_REF] Muschet | Removing the bottlenecks of cell culture metabolomics: fast normalization procedure, correlation of metabolites to cell number, and impact of the cell harvesting method[END_REF], quenching [START_REF] Kapoore | Influence of washing and quenching in profiling the metabolome of adherent mammalian cells: A case study with the metastatic breast cancer cell line MDA-MB-231[END_REF][START_REF] Teng | A direct cell quenching method for cell-culture based metabolomics[END_REF] and extraction [START_REF] Dettmer | Metabolite extraction from adherently growing mammalian cells for metabolomics studies: Optimization of harvesting and extraction protocols[END_REF][START_REF] Ser | Extraction parameters for metabolomics from cultured cells[END_REF][START_REF] Martineau | Strategy for choosing extraction procedures for NMR-based metabolomic analysis of mammalian cells[END_REF], with little evaluation of their inter-connections and integration into the global procedure. In addition, protocols have been mostly exemplified on single cell lines, which differ across studies. Many questions therefore remain regarding the actual range of parameters that have significant effect on metabolite extraction yields.

Growth media used for mammalian cell culture have a rich composition to supply cells with nutrients required for maintenance, growth and proliferation. Media removal is a perquisite for cell extraction to avoid contamination of extracts by exogenous compounds. The fast kinetics of cell metabolism with respect to experimental manipulation leads to strong metabolic perturbations within span of seconds after medium removal [START_REF] De Koning | A method for the determination of changes of glycolytic metabolites in yeast on a subsecond time scale using extraction at neutral pH[END_REF][START_REF] Villas-Bôas | Metabolome Analysis: An Introduction[END_REF]. Metabolites such as Glucose, ATP and ADP have turnover rates of millimolar per seconds [START_REF] De Koning | A method for the determination of changes of glycolytic metabolites in yeast on a subsecond time scale using extraction at neutral pH[END_REF][START_REF] Rizzi | In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae: II. Mathematical model[END_REF][START_REF] Schwiebert | Extracellular ATP as a signaling molecule for epithelial cells[END_REF], while others are volatile, or quickly degraded by external factors such as light exposure [START_REF] Villas-Bôas | Metabolome Analysis: An Introduction[END_REF]. Meanwhile, leakage of metabolites from the intracellular medium into the washing solution may also affect metabolomic measures. Due to their small molecular size, metabolites are easily lost from cells by diffusing through cell membrane and are secreted in the washing solution. This is especially the case when the solution has different osmotic strength than the growth medium [START_REF] Kapoore | Influence of washing and quenching in profiling the metabolome of adherent mammalian cells: A case study with the metastatic breast cancer cell line MDA-MB-231[END_REF][START_REF] Britten | The amino acid pool in Escherichia coli[END_REF]. For this reason, PBS was shown to be a better washing solution than other commonly used solvents like water, even if metabolites loss is inevitable [START_REF] Ser | Extraction parameters for metabolomics from cultured cells[END_REF]. While the whole procedure may be carried out in a cold room to slow down metabolism and minimize thermal shock [START_REF] Kostidis | Quantitative NMR analysis of intra-and extracellular metabolism of mammalian cells: A tutorial[END_REF], this may turn out impractical and in practice the use of either room-temperature PBS or ice-cold PBS is often favoured, with a number of successive washes varying across studies [13, 15-17, 19, 22, 23, 25, 32-34]. In addition, metabolism still occurs until metabolite quenching which further changes metabolic profiles.

Optimization and evaluation of protocols designed to avoid the contamination from exogenous growth media while minimizing metabolite loss prior to quenching therefore remains a timely issue.

Metabolism quenching possibly stands as the most crucial step towards cellular metabolite extraction.

Quenching aims at stopping enzymatic reactions, hence fix metabolite concentrations in the cells, and can be achieved using a variety of methods: freezing by liquid nitrogen [START_REF] Kostidis | Quantitative NMR analysis of intra-and extracellular metabolism of mammalian cells: A tutorial[END_REF], which is well adapted for tissue extractions [START_REF] Zukunft | High-throughput extraction and quantification method for targeted metabolomics in murine tissues[END_REF][START_REF] Beckonert | Metabolic profiling, metabolomic and metabonomic procedures for NMR spectroscopy of urine, plasma, serum and tissue extracts[END_REF], addition of a quenching solvent discarded thereafter, mostly used for suspension cell cultures [START_REF] Sellick | Metabolite extraction from suspension-cultured mammalian cells for global metabolite profiling[END_REF], or addition of a dual-role solvent that simultaneously quench and extract metabolites. For adherent mammalian cells, the latter method is most frequently privileged, as the easiest to implement, without loss of metabolites [START_REF] Kapoore | Cell line dependence of metabolite leakage in metabolome analyses of adherent normal and cancer cell lines[END_REF]. Treatment with cold methanol was shown to quench the metabolism and disrupt the cell membrane causing at the same time extraction of metabolites [START_REF] Teng | A direct cell quenching method for cell-culture based metabolomics[END_REF].

Carried out before or after quenching, cells harvesting aims at recovering the complete cellular matter from the culture dish. This is typically achieved either by cells scraping or trypsinisation. While scraping is performed on quenched cells, trypsinization is carried out prior to quenching and imposes strong physiological and mechanical stress through interaction of trypsin with membrane proteins to detach cells, and was shown to induce strong perturbations on the cellular metabolism [START_REF] Teng | A direct cell quenching method for cell-culture based metabolomics[END_REF]. Several studies have compared both strategies and have shown that scraping the cells achieved better extraction yield and weaker metabolite loss compared to trypsinization [START_REF] Dettmer | Metabolite extraction from adherently growing mammalian cells for metabolomics studies: Optimization of harvesting and extraction protocols[END_REF][START_REF] Bi | Optimization of harvesting, extraction, and analytical protocols for UPLC-ESI-MS-based metabolomic analysis of adherent mammalian cancer cells[END_REF][START_REF] Teng | A direct cell quenching method for cell-culture based metabolomics[END_REF]. Consequently, scraping has become the commonly used harvesting method over the past few years. Yet, it can lead to variable amounts of recovered cells between samples, especially when manipulating small diameter or fragile containers such as inserts, or when cells tend to form aggregates upon scraping. Kapoore et al. notably demonstrated that both trypsinization and scraping lead to metabolite loss that is dependent on cell type [START_REF] Kapoore | Cell line dependence of metabolite leakage in metabolome analyses of adherent normal and cancer cell lines[END_REF]. Extraction (stricto sensu) of metabolites is the last ensemble of steps that aims at recovering metabolites from the different cell compartments in a non-selective and non-destructive way. It is achieved using an extraction solvent and potentially further cell disruption by vortex or sonication. A wide variety of extraction methods were described for metabolomics studies [START_REF] Hutschenreuther | Comparison of extraction conditions and normalization approaches for cellular metabolomics of adherent growing cells with GC-MS[END_REF][START_REF] Teng | A direct cell quenching method for cell-culture based metabolomics[END_REF][START_REF] Muschet | Removing the bottlenecks of cell culture metabolomics: fast normalization procedure, correlation of metabolites to cell number, and impact of the cell harvesting method[END_REF][START_REF] Cao | GC-TOFMS analysis of metabolites in adherent MDCK cells and a novel strategy for identifying intracellular metabolic markers for use as cell amount indicators in data normalization[END_REF]. Pure methanol, aqueous methanol, or a mixture of methanol, water and chloroform (biphasic extraction) were shown to be reliable and efficient extraction blends leading to better extraction yields than other solutions such as perchloric acid or a mixture of water and acetonitrile [START_REF] Martineau | Strategy for choosing extraction procedures for NMR-based metabolomic analysis of mammalian cells[END_REF][START_REF] León | Mammalian cell metabolomics: Experimental design and sample preparation[END_REF]. However, contradictive reports are found regarding the efficiency of methanol or aqueous methanol extraction over the two-phase extraction protocol [START_REF] Dettmer | Metabolite extraction from adherently growing mammalian cells for metabolomics studies: Optimization of harvesting and extraction protocols[END_REF][START_REF] Lorenz | Reducing time and increasing sensitivity in sample preparation for adherent mammalian cell metabolomics[END_REF][START_REF] Bi | Optimization of harvesting, extraction, and analytical protocols for UPLC-ESI-MS-based metabolomic analysis of adherent mammalian cancer cells[END_REF]. Biphasic extraction using methanol, chloroform and water has become arguably the most commonly used approach for cellular extraction. However, this method presents weaknesses associated with manipulation of toxic and volatile chloroform, and requires use of glassware little suited to high-throughput studies.

Overall practicality, and ergonomics in general, of existing protocols was given little pondering in previous studies. Yet, it impacts not only the feasibility of protocols in different laboratory settings, but also the more global accuracy, reproducibility and scalability of cell metabolic fingerprinting studies. As metabolomics has been rapidly democratizing as a standard tool for cell phenotyping, biologists face a recognizable need for generic, fast and efficient protocols, easily manageable by the non-metabolomics experts.

Here, we present a fast and ergonomic protocol for metabolite extraction from adherent mammalian cell cultures, tailored for in vitro NMR-based metabolomics studies and applicable to broader analytical strategies. The proposed method results from optimization of all washing, quenching and extraction steps, after evaluation of individual or combined sets of parameters. The protocol efficacy is assessed for eight different adherent mammalian cell lines, and its reproducibility is evaluated for HeLa cells by four different operators with reference to biphasic extraction. The proposed protocol comprises a limited number of simple steps, and balances efficient extraction of intracellular metabolites with minimum contamination from growth medium and minimum leakage of metabolites from the cells. It is fast, manageable without specific training, and easily automatable and scalable to small cell cultures in well plates for high-throughput studies. This optimized protocol aims at providing a suitable basis for sample preparation for broad metabolomic phenotyping characterization of central metabolism, across mammalian cell types.

MATERIALS AND METHODS

Materials. HeLa (Human cervical cancer cells), CACO2 (Human colorectal adenocarcimona cells), C2C12 (Mouse myoblasts), HEK 293 (Human embryonic kidney epithelial cells), 3T3-L1 (Mouse embryo fibroblasts), CHO-K1 (Hamster ovarian epithelial cells) were originally obtained from ATCC. INS-1E (Rat pancreatic ß cells) were a generous gift from Pr. P. Maechler (University Medical Center, Geneve, Switzerland) [START_REF] Merglen | Glucose Sensitivity and Metabolism-Secretion Coupling Studied during Two-Year Continuous Culture in INS-1E Insulinoma Cells[END_REF][START_REF] Dingreville | Differential Effect of Glucose on ER-Mitochondria Ca2+ Exchange Participates in Insulin Secretion and Glucotoxicity-Mediated Dysfunction of β-Cells[END_REF]. HuH7 (Human hepatocellular carcinoma) cells were a gift from G. Mithieux's laboratory (Inserm U855, Lyon, France) [START_REF] Rieusset | Disruption of calcium transfer from ER to mitochondria links alterations of mitochondria-associated ER membrane integrity to hepatic insulin resistance[END_REF].

Dulbecco's Modified Eagle's medium (DMEM) and RPMI were purchased from Gibco. Penicillinstreptomycin solution for cell culture and Foetal bovine serum (FBS lot BCBW7811) were purchased from Sigma-Aldrich. Dubelcco's Phosphate Buffered Saline (DPBS) 1x without calcium and without magnesium was purchased from Dominique Dutscher. Deuterium oxide (D2O, 99.8%D) was obtained from Eurisotop. Lactate standard (TraceCERT ® , 1000 mg/L) for metabolite quantification was obtained from Sigma-Aldrich. All other reagents were of analytical grade.

Cell culture. INS-1E cells were cultured in RPMI-1640 culture medium containing 11 mM glucose supplemented with 5% of heat-inactivated FBS, 2 mM glutamine, 10 mM HEPES, 1 mM Sodium Pyruvate, 100 U/ml penicillin, 100 µg/ml streptomycin and 50 µM ß-mercaptoethanol (Sigma), at 37° C in a humidified atmosphere containing 5% CO2. HuH7 cells were cultured in DMEM (1 g/L glucose) supplemented with 10% FBS, 100 U/ml penicillin, 100 µg/ml streptomycin, at 37° C and 5% CO2. The six other cell lines (HeLa, CACO2, C2C12, HEK 293, 3T3-L1, CHO-K1) were cultured in DMEM (4.5 g/L glucose, 2 mM glutamax) supplemented with 10% FBS, 100 U/ml penicillin, 100 µg/ml streptomycin, at 37°C and 5% CO2. Cells were seeded in 10-cm petri dishes to reach 80% confluence after 3 days to perform metabolome extraction.

Cell extraction and protocol optimization.

For the recovering of metabolite extracts, cell plates were processed by batches of three for all critical steps (washing, quenching and extraction) and their optimisation, as a compromise between processing throughput by repetition of identical tasks, and minimisation of the global processing time for each sample. In this work, all steps for metabolite extraction were optimized sequentially: cells washing, quenching, harvesting, extraction. Evaluated protocols are further detailed throughout the results section. Extraction yields for 27 quantified metabolites were used to evaluate protocols efficiency. Optimizations of the different parameters for all extraction steps, and assessment of the protocol efficiency on multiple cell lines were conducted for at least three biological replicates for each condition and by the same operator to exclude experimental bias. Biphasic extraction using methanol, chloroform and water stands in this work as the "reference" protocol, detailed in Figure 1, and is adapted from the method described by Beckonert et al. for tissue extraction [START_REF] Beckonert | Metabolic profiling, metabolomic and metabonomic procedures for NMR spectroscopy of urine, plasma, serum and tissue extracts[END_REF].

NMR Sample Preparation.

After extraction, raw metabolite extracts were dried under a gentle N2 flow until complete evaporation, then stored at -20°C until NMR sample preparation, right before analysis. vortex for 30 s. Extracts were then transferred to 1.5 ml Eppendorf tubes and centrifuged at 13000 rpm for 1 minute at 4°C. 550 μl of supernatant was transferred to 5 mm NMR tubes using a TECAN Evo 75 liquid handler.

NMR Spectroscopy.

All NMR experiments were recorded on a Bruker Avance III spectrometer operating at 600.13 MHz ( 1 H resonance frequency), equipped with a triple resonance TCI cryoprobe and cooled (4°C) in a SampleJet sample changer. After automatic tuning and shimming, 1 H NMR profiles of cell extracts were acquired for each sample using a one-dimensional NOESY with gradients and water presaturation (pulse program noesygppr1d). The sample temperature was regulated at 27°C. The relaxation delay was set to 3 s, and the NOESY mixing time to 10 ms. 128 transients were co-added, with an acquisition time of 2 s and a spectral width of 20 ppm. After Fourier transformation using an exponential line-broadening of 0.3 Hz, spectra were manually phased, baseline corrected, and referenced to the glucose signal at 5.23 ppm using Topspin (Bruker GmbH, Germany). Two-dimensional experiments including 1 H JRES, 1 H-1 H TOCSY and 1 H- 13 C HSQC were additionally recorded on a set of representative samples for metabolites annotations. S1, ESI), metabolite concentrations in cell extract samples were exploited to evaluate step-by-step optimizations (washing, quenching, extraction parameters), as well as extraction protocols in their globality. Metabolite quantification was carried out from 1D 1 H NMR spectra. Relative quantifications were obtained by highthroughput integration of well resolved peaks corresponding to 27 metabolites using the Amix software (Bruker GmbH) for each spectrum from all studied cell lines (total 224 spectra). A synthetic reference signal for quantification, defined from the 1 H spectrum of an external 3.36 mM lactate standard, was inserted in each spectrum using the ERETIC 2 method [START_REF] Akoka | Concentration measurement by proton NMR using the ERETIC method[END_REF] implemented in Topspin. Subsequently, interactive deconvolution of the NMR profiles using the Chenomx NMR Suite 8.2 (Chenomx Inc., Edmonton, Canada) provided a precise quantification of 41 metabolites in each sample for comparison of the optimized and reference extraction protocols on HeLa cells. Measured concentrations of metabolites in NMR samples range from a few micromolar to hundreds micromolar. Total quantity of matter was also evaluated by integration of the full spectrum to globally assess the extraction yield for each procedure.

Metabolites quantification. Following metabolite identification (Table

RESULTS

The different steps for metabolite extraction from adherent mammalian cells were optimized sequentially after downsizing protocol variables according to previous literature described above. Tested conditions for HeLa cells extraction were systematically compared to the reference protocol (Figure 1a). All extracts were analysed by 1D 1 H NMR spectroscopy for metabolite quantification. A representative spectrum with metabolite annotations in presented in Figure 2.

Evaluation of washing methods.

Variable volumes of warm PBS and number of washes were tested to assess contamination from residual growth media after its removal by pipetting: a single 3 ml PBS wash, a single 6 ml PBS wash, 2 washes with 3ml PBS each, a 6 ml wash followed by a 3 ml wash, and 3 washes with 3 ml PBS. The different washing solutions were analysed by NMR spectroscopy after removal from the culture dish (Figure 3a). Remarkably, the total quantity of matter measured in the washes increases with both the total volume of PBS used and the number of successive washes, showing that metabolites may originate not only from residual growth medium, but also largely from leakage and secretion from the cells.

Since the timespan required to carry out multiple washes prior to quenching can reach minutes, we also examined intracellular metabolism kinetics on this timescale for a representative cellular nutrient (glucose) after growth medium removal. For this, we replaced the growth medium with a glucosedepleted medium before carrying out cellular extraction (with full protocol). This allows to quantify intracellular glucose at different time points following medium replacement. Figure 3b shows a sharp decrease of intracellular glucose within one minute of medium replacement. After 1 minute of glucose deprivation (30" of culture in glucose depleted-medium + 30" for medium removal and washing prior to quenching), intracellular glucose level has dropped 5-fold compared to 30" glucose deprivation.

Intracellular glucose concentration reaches a low plateau after 1.5 minute glucose deprivation in the media. Such rapid time-scale implies that multiple time-consuming washes prior to quenching should be avoided.

Evaluation of quenching and extraction methods.

In order to assess the possibility of disentangling the quenching and extraction steps in our protocol, we first evaluated a method proposed by Sellick et al. for the case of suspension-cultured cells [START_REF] Sellick | Metabolite extraction from suspension-cultured mammalian cells for global metabolite profiling[END_REF]. The method uses 60% cold methanol supplemented with 0.85% (wt/vol) AMBIC, where AMBIC is tentatively recruited to protect cellular membranes, therefore blocking metabolism without emptying cells from their metabolite content. After quenching, this solution is to be discarded. Here, we recovered the mixture to determine the quantity of metabolite leaked into the quenching solution. Our data show a clear loss of metabolites using this approach (Figure S1, ESI), with no practical advantage to use such separate quenching steps in the case of adherent cells. We stress that all quenching approaches intrinsically impact, to some extent, the integrity of cellular membranes. Hence, quenching and extraction should hardly be considered as possibly independent steps in the whole procedure. In the following, we used a combined quenching and extraction step by cold methanol.

We then evaluated the conventional method that includes, directly after quenching, harvesting cells by scraping the culture dish against a protocol that skips this step. We hypothesized that polar metabolites are in fact completely extracted into methanol (or aqueous methanol) during the quenching/extraction step, making manual recovery of the cell debris unessential. Three groups of samples were assessed and the corresponding results are presented in Figure 4. For the first group, 3 ml methanol was spread across the dish by a tilting motion repeated three times, then transferred into a glass tube, without scraping. The dish was rinsed with 1ml methanol, and the solution pooled with the primary extract. For the second group, cells were detached from the dish using a cell lifter directly after addition of 3 ml of cold methanol. The mixture of solvent and cell debris were then transferred into a glass tube, and the dish was rinsed with 1 ml methanol for full recovery of cellular material. The third reproduced the same protocol with cell scraping using a methanol/water 3:1 (v/v) solution as extraction solvent. Scraping the cells had no significant effect on the majority of metabolites (Figure 4), with increased yield for only 6 metabolites out of 27 when harvesting the cells with a lifter. These are mainly purine and (5'-5')dinucleotides as well as myo-inositol and some derivatives of carboxylic acids (glutathione, creatine), present at concentrations less than 0.1 mM in the cellular extracts. The combination of scraping with the use of aqueous methanol as an extraction solvent permitted to retrieve significantly higher concentrations for only 7 metabolites out of 27 than when using a simple extraction with methanol, without scraping. Glutamine was the most impacted metabolite.

We then further refined our assessment of extraction parameters, by probing altogether the nature of extraction solvent (methanol or methanol/water 3:1), the number of successive extractions (1, 2 or 3), total contact time between extraction solvent and cells (0, 3, or 6 minutes), and the total volume of extraction solvent (4 or 7 ml; volumes were chosen to allow complete coverage of the 10 cm dish at the initial quenching step). Corresponding results are summarized in Figure 5, and show that increasing the contact time between the extraction mixture and cells did not impact the extraction yield (Figure 5a). The use of a 3 + 1 mL methanol extraction gave optimal yields for 18 out of 27 metabolites. From all the above observations regarding washing, quenching and extraction, together with considerations of protocol ergonomics and rapidity of execution, we defined an optimized protocol based on a simple methanol extraction without scraping (Figure 1). The proposed protocol was further evaluated in reference to conventional water/methanol/chloroform extraction by a detailed quantification of 41 extracted metabolites in Hela cells (Table S2 & Figure S2, ESI), before assessment in different cell lines.

Efficacy of the optimized protocol in eight cell lines.

The optimized and reference protocols were compared for metabolite extraction in eight different cells lines (Figure S3, ESI). In seven cell lines (Hela, HuH7, INS-1E, C1C12, HEK 293, 3T3-L1, and CACO2), our fast (optimized) protocol showed excellent yields with respect to the reference, providing better or equivalent extraction for the majority of metabolites. Higher levels of amino-acids were in particular recovered. However, levels of acetate, formate, ethanol and nucleotides were overall increased in extracts following the reference method. In contrast, the optimized protocol showed a relatively poor performance for metabolite extraction in CHO-K1 cells (ovarian epithelial cells).

Intra-and inter-operator reproducibility of the optimized and reference methods.

Intra-and inter-operator reproducibility assessment for both the optimized and reference extraction protocols was achieved by comparing HeLa extracts obtained by four different operators in quadruplicates. Intra-and inter-operator reproducibility may reflect the respective protocols' ergonomics.

Samples were prepared by the different operators in the same laboratory, with identical consumables, in the span of a single day. When comparing measured metabolites concentrations between operators, we observed a comparable stability of the measures for most metabolites using the two protocols. A larger intra-operator variability is observed with the reference protocol for a number of metabolites, in particular acetate, isobutyrate, lactate, and myoinositol (Figure S4, ESI). We note that the standard deviation across replicates, one component of intra-operator reproducibility, is also an individual characteristics of the operator, with operator 2 remarkably providing more stable results than others for both protocols. Inter-operator reproductibility is higher in the case of the optimized protocol for almost all metabolites (Figure S5, ESI). These data overall emphasize the robustness of our proposed method.

DISCUSSION

Evaluation of the endometabolome in mammalian adherent cells is naturally challenging, due to the structural diversity of cellular metabolites, their broad dynamic range, and cellular compartmentalization.

Different cell lines display structural specificities in their membranes and given cellular functions associated with variable rates of enzymatic reactions that further complicates this task. Although no single method allows complete extraction of all classes of metabolites from mammalian cells, advanced knowledge on how extraction procedures may affect metabolite recovery is key to their optimization. Subsequently, extraction protocols may be modulated to suit the characteristics of specific cell lines and objectives of given metabolomic studies that either focus on pre-defined metabolite classes, or aim at untargeted evaluation of the broad intracellular metabolome.

Our data demonstrated that although eliminating growth media residues by washing is a necessary step to obtain meaningful endometabolome profiles, time remains a critical point. Metabolite depletion by active metabolism in the cell may have more deleterious impact than residual contamination from growth media, and time-consuming steps before quenching have substantial effects on metabolite extraction yields. We showed that a suitable compromise is achieved with a single step wash with warm PBS immediately followed by cold methanol quenching, in agreement with previous literature that showed a single PBS wash was less damaging than two consecutive washes [START_REF] Kapoore | Influence of washing and quenching in profiling the metabolome of adherent mammalian cells: A case study with the metastatic breast cancer cell line MDA-MB-231[END_REF][START_REF] Lu | Metabolite Measurement: Pitfalls to Avoid and Practices to Follow[END_REF]. We chose a PBS volume of 6 ml to stronger dilute residual material from growth medium and minimize contamination as compared to a single 3 ml wash. We note that regardless any efforts made to minimize pre-quenching delays, measured concentrations of metabolites in extracts cannot flawlessly reflect actual intracellular concentrations at the time of sampling, as the decrease of intracellular nutrients is most important during the first seconds after media removal. Measured metabolite levels can either under-or over-estimate true intracellular concentrations, due to leakage into the washing solution or conversion/degradation of metabolites by ongoing enzymatic reactions. Optimally, operators should manipulate one dish at a time to ensure that the quenching time-point remains minimal and constant, with pre-quenching steps contained within a 30 s timespan. However, high-throughput studies require batch processing, and protocols suitable for automatization.

For this reason, the specific added-value of manual cells scaping after quenching/extraction was investigated. Our data showed that most metabolites are suitably extracted by simple addition of methanol, without scraping, which paves the way for a fast, ergonomic and scalable protocol for cellular metabolite extraction. The absence of scraping also contributes to reproducibility of the procedure, and the presence of residual cellular material in the dishes after quenching/metabolite extraction allows further complementary use of this material, notably for imaging purpose (Figure S6, ESI). We note that despite efficient quenching properties, addition of methanol may generate artefacts, as described by Sauerschnig et al., and therefore proper storage of extracts at -80°C is required immediately after extraction until measurement [START_REF] Sauerschnig | Methanol Generates Numerous Artifacts during Sample Extraction and Storage of Extracts in Metabolomics Research[END_REF]. This is also important since incomplete quenching from partial denaturation of enzymes cannot be fully excluded [START_REF] Lu | Metabolite Measurement: Pitfalls to Avoid and Practices to Follow[END_REF]. Surprisingly, we found that large volumes of extraction solvents and increased number of successive extractions did not permit the recovery of a greater amount of quantified metabolites, and the use of 3 ml + 1 ml of solvent gave optimal results. Remotely from the actual extraction efficiency, this may be explained considering the drying step that precedes re-dissolution of extracts into the NMR buffer. Along this process, dry metabolite mixture is coated over the internal surface of the sampling tubes. For the largest volumes of extraction solvents, metabolites are therefore scattered over larger surfaces, which hinders subsequent re-dissolution into the small buffer volume (typically < 650 μl). To avoid loss of metabolites at this stage, the use of an extraction volume adapted to both the surface of the cell culture dish and the final re-dissolution volume of dried extracts is required. Gentle dissolution of dry residuals from top parts of the tubes by manual rocking throughout evaporation under N2 gas may also minimize metabolites loss.

Whereas the use of water in extraction mixture provides better extraction for some classes of metabolites (mainly nucleotides) as compared to pure methanol, addition of water considerably lengthens the drying of extracts by N2 gas, due to lesser volatility. The presence of water in the extraction solvent was also associated with greater variability between replicate measures for a number of metabolites such as myo-inositol, acetate, NADH, ATP+ADP, or AMP, while the use of pure methanol led to optimal intra-and inter-operator reproducibility. In the case of NAD+ and NADH, the individual values of concentrations alone are not of biological importance contrary to their ratio. Scraping the cells and using water in the extraction mixture induced a strong shift on the measured NAD+/NADH ratio, diverging from physiological values in the cell (Figure 4).

While the present study does not comparatively evaluate strategies for drying metabolite extracts, we stress that alternative methods to gentle evaporation under N2 gas flow can be employed, such as lyophilisation, or evaporation using a centrifugal vacuum concentrator. We note that availability of such devices in biology laboratories often governs the actual choice of drying method.

In the present study, we evaluated the efficiency of the reference and optimized extraction protocols in eight different cell lines, selected to cover diverse properties like tissue origin and function, main secreted metabolites classes, as well as size and membrane properties of the cells. Our results show the proposed optimized fast protocol provides efficient metabolite extraction for most cell lines, with the exception of CHO-K1 cells. Comparative detailed performance of the pure methanol vs. biphasic extraction yet depends on cell lines, and may be associated with variable subcellular compartmentation, such as differentially developed endoplasmic reticulum, or the abundance of lipid storage in droplets.

Ideally, extraction protocols should therefore be optimized for each cell line.

Overall, our optimized protocol represents a good balance between the simplicity of the method and the metabolite extraction yield. We reduced by half the number of steps from media removal to sample drying, as compared to biphasic reference extraction, while avoiding the use of toxic and volatile chloroform and manual cells scraping and separation of polar and organic phases, to the benefit of protocol rapidity, ergonomics and reproducibility. Whenever care must be taken for extraction of specific metabolite classes, such as nucleotides, minor adjustment the protocol such as individual addition of a scraping step or water in the extraction solvent may provide useful alternatives. This fast and ergonomic protocol to characterize the intracellular metabolome is also compatible with exometabolomic investigations of adherent cell lines. Altogether exo-and endo-metabolomes are relevant to elucidate mechanistic aspects of cellular physiopathology.

CONCLUSION

Adherent mammalian cell lines display wide differences in structure and membrane properties. They contain metabolites from different classes, with widely diverse properties of solubility, polarity, volatility, and chemical stability. While metabolite extraction procedures may be fine-tuned for each given cell line, general guidelines and protocols implementable by non-metabolomics experts are needed to promote accessibility of metabolomic investigations to the broad biological community.

Here, we demonstrated a fast and ergonomic protocol for adherent mammalian cell metabolite extraction towards NMR detection and quantification, by optimization of the pre-quenching, quenching and extraction steps. The proposed procedure minimises metabolite leakage, and simultaneously quenches metabolism and extracts a wide range of metabolites with a limited number of steps. It is easily implementable, scalable and automatable, and shown to be highly reproducible and effective for a broad range of cell lines. The protocol remains versatile as it can be easily modulated by minor modifications (addition of water in extraction solvent and/or optional cell scraping step) to meet specific needs for targeted metabolite studies. We promote the proposed methanol-based fast extraction procedure as a method of choice towards large-scale metabolomic studies in cells. For the conventional protocol (a) the dish is first rinsed with 1 ml cold methanol, then cells are collected with a cell lifter and transferred into a glass tube, before 4 ml chloroform and 3.6 ml water are added to the cell suspension. After separation by gentle centrifugation (15 min at 4°C at 5000 rpm), the polar (i.e. top phase) and organic (bottom phase) fractions are collected individually. Our optimized protocol (b) includes a combined quenching and extraction step using methanol (3 + 1 ml), without cell scraping. For both protocols, the obtained polar fractions are finally dried under a gentle N2 gas flow (alternatively, lyophilisation or Speedvac can be used) until complete evaporation. Dried extracts are re-dissolved in 650 μl NMR buffer prepared as described by Beckonert et al. [START_REF] Beckonert | Metabolic profiling, metabolomic and metabonomic procedures for NMR spectroscopy of urine, plasma, serum and tissue extracts[END_REF], vortexed for 30 s, and centrifuged (13000 rpm, 4°C, 1 min) in a 1.5 ml microtube. 550 μl of the supernatant is then transferred into a 5 mm NMR glass tube for metabolic profiling.

Figure

  Figure 5b illustrate the sensitivity to extraction solvent volume, and fractionation of extraction. For a given total volume of extraction solvent, the use of successive extractions tended to increase extraction yields, however increasing the total volume of methanol from 4 to 7 mL did not have a positive impact.

Figure 1 :

 1 Figure1: Schematic cell extraction protocols for NMR metabolomic investigation of adherent mammalian cells. For both reference (a) and optimized (b) methods, growth medium is first removed from the culture dish, before cells washing with 6 ml PBS, and quenching with 3 ml ice-cold methanol.

Figure 2 :

 2 Figure 2: Representative 1 H NMR spectrum (600 MHz) for a HeLa cells extract with metabolite annotations, as obtained using our optimized protocol. Abbreviations: Bet: Betaine, ChoP: Phosphocholine, Glp: Pyroglutamate, GSH: Glutathione, NAC1: N-acetyl 1, MI: Myoinositol, PCr: Phosphocreatine, Pyr: Pyruvate, UDP-Gal: UDP-galactose, UDP-Glc: UDP-glucose, UDP-GlcNAc: UDP-N-acetyl-glucosamine

Figure 3 :

 3 Figure 3: Sensitivity to washing parameters. (a) Total quantity of metabolites represented by total intensity of spectra in PBS washes recovered after washing the cells with different PBS volumes and number of washes; (b) Intracellular glucose concentration in the cells, as measured from extracts, after different times without contact with extracellular glucose. The total duration of pre-quenching steps is 30 s, corresponding to cell washing (once) with 6 ml PBS. The point at time zero in the graph represents a projected glucose concentration at the instant of media removal, not measurable. Error bars represent +/-standard deviation from 3 biological replicates.

Figure 4 :

 4 Figure 4: Metabolite concentrations in extracts as a function of cell harvesting method (with or without cells scraping) and solvent nature (methanol 3+1 ml, or methanol 3ml + water 1 ml). (a) Metabolites for which scraping after extraction with methanol or aqueous methanol does not significantly impact the concentration in extracts and (b) metabolites which concentrations are significantly impacted by scraping and/or extraction with water in addition to methanol. Six biological replicates were considered for each protocol; error bars represent +/-standard deviation. * significant variations between the two protocols (Student t-test p-values < 0.05).

Figure 5 :

 5 Figure 5: Sensitivity to extraction parameters (a) Overview of fold change for the concentration of metabolites extracted with a range of extraction procedures using different solvents for extraction and increasing contact times between solvents and cells, with reference to an extraction by twice 3 ml methanol followed by 1 ml methanol, and no waiting time; (b) Overview of fold change for metabolites extracted with different extraction procedures, varying total solvent extraction volumes and number of successive extractions. Three biological replicates were considered for each protocol.

Figure 2 Figure 3

 23 Figure 2

Conflict of Interest

The authors declare no conflict of interest.


Carlos Quesada

Claire Dupont

Pierre Villon

Anne-Virginie Salsac
email: a.salsac@utc.fr

Keywords: Identification, mechanical properties, microcapsules, data-driven method, diffuse approximation

A novel data-driven real-time procedure based on diffuse approximation is proposed to characterize the mechanical behavior of liquid-core microcapsules from their deformed shape and identify the mechanical properties of the submicron-thick membrane that protects the inner core through inverse analysis. The method first consists of experimentally acquiring the deformed shape that a given microcapsule takes at steady-state when it flows through a microfluidic microchannel of comparable cross-sectional size. From the mid-plane capsule profile, we deduce two characteristic geometrical quantities that uniquely characterize the shape taken by the microcapsule under the external hydrodynamic stresses. To identify the value of the unknown rigidity of the membrane and the size of the capsule, we compare the geometrical quantities to the values predicted numerically using a fluid-structure-interaction model by solving the threedimensional capsule-flow interactions. The complete numerical data set is obtained off-line by systematically varying the governing parameters of the problem, i.e. the capsule-to-tube confinement ratio and the capillary number, ratio of the viscous to elastic forces. We show that diffuse approximation efficiently estimates the unknown mechanical resistance of the capsule membrane. We validate the data-driven procedure by applying it to the geometrical and mechanical characterization of ovalbumin microcapsules (diameter of the order of a few tens of microns). As soon as the capsule is sufficiently deformed to exhibit a parachute shape at the rear, the capsule size and surface shear modulus are determined with an error of only 0.2% and 2.7%, respectively, as compared to 2-3% and 25% without it, in the best cases (Hu et al. PRE 2013). Diffuse approximation thus allows to quasi-instantly provide the capsule size and resistance with a very high precision. It opens interesting perspectives for all the industrial applications that require a tight control of the capsule mechanical properties in order to secure their behavior when they transport active material.

Introduction

A capsule is a liquid droplet enclosed within a thin elastic membrane. Capsules are found in nature in the form of cells or eggs, but they can also be artificially synthesized for multiple industrial and clinical purposes (1; 2). The pharmaceutical [START_REF] Yih | Engineered nanoparticles as precise drug delivery systems[END_REF], textile (4), cosmetic [START_REF] Miyazawa | Preparation of a new soft capsule for cosmetics[END_REF] and food industries (6) make a wide use of artificial capsules to control the release of active ingredients (drugs, cells, viruses, ...), aromas or flavors. The capsule radius is typically micrometric, ranging from a few microns to a few tens of microns.

Whether natural or artificial, capsules are always in suspension in an external fluid, which subjects the capsules to hydrodynamic forces when it flows and leads to their deformation. The dynamic behavior of capsules is thus governed by three-dimensional fluid-structure interactions, in which the membrane plays a crucial role. It ensures the protection and transport of the internal content, the control of its potential release and the deformability of the capsule thanks to its thinness and elastic resistance. However, the small size and fragility of the microcapsule make the assessment of its mechanical properties a challenging task. Different experimental methods exist to deform micrometric capsules and estimate the mechanical properties. For individual cells and vesicles, micropipette aspiration is the most used technique [START_REF] Needham | The mechanochemistry of lipid vesicles examined by micropipet manipulation techniques[END_REF]. The mechanical properties are obtained by aspirating the particle into a micropipette at different pressure conditions and measuring the resulting deformation. Atomic Force Microscopy (AFM) can also be used to deform capsules under known forces [START_REF] Fery | Mechanical properties of microand nanocapsules: Single-capsule measurements[END_REF]. For capsule populations in suspension, more recent techniques have been developed based on microfluidic experiments. They consist in flowing the capsules through a microchannel in order to apply inverse analysis techniques to the observed deformed profiles (9; 10; 11).

In all the cases, a numerical model is needed to determine the values of the mechanical properties. For the microfluidic experiments, numerical simulations based on the resolution of complex fluid-structure interactions (12; 13; 14) provide the deformed profile of the capsules at steady-state. However, identifying the mechanical properties of a capsule by comparing its deformation with those obtained in the numerical simulations remains challenging. None of the existing studies proposed a consistent method to solve the inverse problem.

In this work, we present a fast, accurate, self-contained technique for inverse analysis using a data-driven method based on the diffuse approximation [START_REF] Nayroles | Generalizing the finite element method: diffuse approximation and diffuse elements[END_REF]. We focus on experimental data obtained by flowing a microcapsule in microfluidic square-section channel of comparable size. The experimental data consists of the capsule velocity and mid-plane profile at steady-state, from which we deduce geometrical quantities (e.g. maximum extension length and axial length) that are characteristic of it. Numerical models of this exact problem exist (16; 13). The one by Hu et al. [START_REF] Hu | Flow of a spherical capsule in a pore with circular or square cross-section[END_REF] is used off-line to get a complete numerical data-set of the three-dimensional steady-state shapes adopted by the capsule inside the microchannel for a wide range of values of the input parameters: the size ratio, which corresponds to the capsule-to-tube confinement ratio, and the capillary number, ratio of the viscous friction force acting onto the capsule to the restoring membrane elastic force. A database of twodimensional capsule contours (cross-cuts) is obtained from these numerical simulations along with their geometrical quantities. The algorithm used to identify the mechanical properties of the capsules consists of applying the diffuse approximation method to the numerical database to deduce the size ratio and capillary number that correspond to the measured values of the geometrical parameters of the capsule profile.

Materials and methods

Problem description

We consider an initially spherical capsule of radius a flowing within a long prismatic microchannel with constant square cross-section of side 2 (Fig. 1). The thin membrane of the capsule is made of an impermeable hyperelastic isotropic material with surface shear modulus G S . As the capsule flows, the hydrodynamic forces inside the channel gradually deform its membrane (Fig. 2). Eventually, the capsule reaches a steady-state shape that is function of the constitutive law of the membrane and two independent parameters:

• The capillary number Ca, defined as

Ca = µ U/G S , (1)
where µ is the viscosity of the external liquid and U is the mean axial velocity of the undisturbed Poiseuille flow. • The size ratio a/ between the capsule radius and the channel cross-dimension.

Our objective is to obtain the value of G S , which is the mechanical property that governs the capsule membrane behavior.

Experimental procedure

A suspension of polydisperse ovalbumin microcapsules of average diameter equal to 50 µm and of submicronic membrane thickness is prepared as described in [START_REF] Edwards-Lévy | Determination of free amino group content of serum albumin microcapsules using trinitrobenzenesulfonic acid: effect of variations in polycondensation pH[END_REF] and injected into a microfluidic system by means of a syringe pump at different flow rates. The microfluidic system consists of a straight channel of square section, 5 mm in length and ∼ 50 µm. It is fabricated in PDMS following the procedure provided in (18; 19). The motion and deformation of each capsule is observed with a microscope connected to a high-resolution high-speed camera. Two-dimensional sideview gray-scale images of capsules are obtained as they flow in the microchannel (Fig. 3a). More technical details on the experimental setup can be found in (9; 10). The deformed profile of the capsules acquired experimentally can be characterized by geometrical quantities that we normalize using the channel characteristic size (Fig. 4). The inverse analysis algorithm proposed here requires the measurement of only two of those quantities:

• The maximum extension of the capsule along the longitudinal axis L z / . • The axial length L a / .

Together, they provide the information on the depth of the parachute depth, L p = L z -L a (Fig. 4), which measures the concavity at the rear part of the capsule, and was shown to relate well with the global deformation of the capsule [START_REF] Gubspun | Characterization of the mechanical properties of cross-linked serum albumin microcapsules: effect of size and protein concentration[END_REF]. It is, however, not appropriate to use it as one of the two geometrical parameters, as the errors of its estimation are much larger than for L z and L a .

The other quantity obtained experimentally is the velocity of the center of mass of the capsule v o . It is determined at steady-state by measuring the position of a specific point on the membrane on successive time frames. Three quantities are, however, unknown:

• The membrane surface shear modulus G S .

• The capsule radius a, which greatly varies from one capsule of the suspension to the next. • The mean undisturbed external flow velocity U , which is impossible to know with precision, since the flow rate provided by syringe pumps always fluctuate a little over time.

Equations governing the forward fluid-structure interaction problem

The inertialess flow of the deformable micrometric capsule along the channel is obtained by solving the Stokes equations in the external (β = 1) and internal fluids (β = 2), together with the membrane equilibrium equation. For the fluid problem, let v (β) , σ (β) and p (β) be the velocity, stress and pressure fields in the two fluids, non-dimensionalized using as characteristic length, /U as characteristic time and G S as characteristic force. The Stokes equations

∇p (β) = Ca∇ 2 v (β) , ∇ • v (β) = 0, β = 1, 2.
(

) 2
are solved in the domain shown in Fig. 1, assuming no flow disturbance far from the capsule (i.e. the velocity field is the one in the absence of capsule at the inlet and outlet of the square channel), a no-slip boundary condition on the channel and capsule walls and the continuity of the normal load on the capsule wall:

(σ (1) -σ (2) ) • n = q, ( 3
)
where n is the unit normal vector pointing towards the external fluid and q is the non-dimensionalized external load per unit area exerted by the fluids on the membrane due to viscous traction. For the solid problem, let τ be the nondimensionalized Cauchy tension tensor, which corresponds to the forces per unit arclength in the plane of the membrane. The local equilibrium equation governing the inertialess membrane is then

∇ s • τ + q = 0, (4)
where ∇ s • is the surface divergence operator.

Numerical model

Eq. 2 and 4, along with the above boundary conditions, are solved with the numerical model described in [START_REF] Hu | Flow of a spherical capsule in a pore with circular or square cross-section[END_REF]. This model, hereafter referred to BI-FE model, couples the Boundary Integral method to solve the fluid flows with the Finite Element method to solve the membrane mechanics.

It is used to obtain an extensive database of steady-state shapes of capsules in flow. The values of the parameters Ca and a/ , as well as the constitutive law that governs the capsule membrane behavior, are the input parameters of the numerical model. The neo-Hookean law, whose strainsoftening behavior under large deformation has proven to be appropriate to describe ovalbumin capsules [START_REF] Chu | Comparison between measurements of elasticity and free amino group content of ovalbumin microcapsule membranes: discrimination of the cross-linking degree[END_REF], is presently considered to model the membrane. The deformed profile of the capsule at steady-state and the velocity ratio v o /U are some of the outputs of the model. A database of M = 137 three-dimensional steady-state deformed capsules has been generated using the numerical model. The different values of Ca and a/ , for which the simulations have been computed, are shown in Fig. 5, and their associated values of v o /U are represented in Fig. 6.

We shall call T the set of points θ i = θ i 1 , θ i 2 , θ i 3 , where the superscript i (for i = 1 . . . M ) refers to the i-th capsule simulation, and where θ i 1 , θ i 2 and θ i 3 refer to its corresponding values of Ca, a/ and v o /U , respectively. The representation of the points of T in the θ-space shows that they all lie on a surface S T (Fig. 7). The contours of all the shapes in the plane x = 0 have then been obtained, for comparison with the experimental profiles. For each of them, the geometrical quantities of their deformed profiles have been computed and added to the database. We shall call L the set of points

λ i = λ i 1 , λ i 2 ,
where the superscript i (for i = 1 . . . M ) identically refers to the i-th capsule simulation, and where λ i 1 and λ i 2 refer to its corresponding values of L z / and L a / (Fig. 8a).

Inverse analysis approach

The inverse analysis method presented here characterizes the mechanical behavior of the capsule membrane by determining the value of its surface shear modulus G S , as well as the capsule radius a and the external flow speed U , using two steps further described below. From the geometrical quantities measured experimentally (L z / and L a / ) and with the help of the database computed using the BI-FE model, we first use a diffuse approximation technique to obtain the unknown values of the capillary number Ca and size ratio a/ , which are the two independent parameters on which the capsule deformation depends. Knowing Ca and a/ , we then determine the velocity ratio v o /U by interpolating the numerical results of Fig. 7. The surface shear modulus G S is finally deduced from the values of Ca and v o /U using Eq. 1, since the velocity of the capsule center of mass v o is estimated from the acquired images and the viscosity of the external liquid µ measured prior to conducting the experiments.

Diffuse approximation

Only the two independent parameters of the problem Ca and a/ are considered when applying the diffuse approximation method. We shall call T the reduced set of points θ i = θ i 1 , θ i 2 . From Fig. 8a, one can notice that the points of L are inclined. To apply diffuse approximation more easily, a rotation of -45°around the axis perpendicular to the plane defined by L and centered on (0,0) is applied. We shall call L the set of points λ i (Fig. 8b). The points of T and L define respectively the surfaces S T and S L . We deduce that any point not present in the database (λ / ∈ L ) but lying on the surface S L corresponds to admissible geometrical quantities that may be obtained experimentally [START_REF] Meng | Nonlinear shapemanifold learning approach: concepts, tools and applications[END_REF].

Using diffuse approximation techniques (15), we map an arbitrary point λ / ∈ L on the surface S L to a corresponding point θ / ∈ T on the surface S T . The idea is to use this mapping to estimate the unknown values of Ca and a/ knowing the values of the experimentally measured geometrical quantities L z / and L a / . To achieve this, diffuse approximation makes use of a local weighted least squares fitting that is valid in a small neighborhood around λ and is based on the points included within it (Fig. 9). Within this domain centered on λ , the coefficients λ j (j = 1, 2) can be locally approximated by the expression

λ j = p(θ) T a j = 1 θ 1 θ 2   a j 0 a j 1 a j 2   , (5)
where p is a vector of independent polynomial functions and a j are the approximation coefficient vectors.

To approximate λ , we weight the contribution of the points λ i (i = 1 . . . M ), contained in the elliptical neighborhood, proportionally to the distance d between the points λ i and λ . Distances are computed as

d i =   2 j=1 γ j λ i j -λ j 2   1 2
.

Prepared using sagej.cls The parameters γ j (for j = 1, 2) are equal to 1 in the case of a circular neighborhood, but in the present case, we used γ 1 = 1 and γ 2 = 0.05 to suit the elongated shape of the surface S L (Fig. 9). The weight assigned to each λ i is chosen to be

w(D) = 2D 3 -3D 2 + 1, if D ≤ 1 0, otherwise ,
where the normalized distance D = d i /δ is 0 for a point in the center of the neighborhood (d i = 0) and 1 for a point located at its boundary (d i = δ). The value of w(D) ranges from 1 to 0, decreasing monotonically as D increases (Fig. 10). To ensure that the system of equations (see below) is not overdetermined, the neighborhood must include more points λ i ∈ L than the number of elements in vector a j (i.e. N > 3 in this case). To meet this constraint, the neighborhood is chosen to have a variable size, but to keep its elliptical shape with fixed proportions in order to always include N = 14 points regardless the position of λ in S L . This is achieved by setting δ (the distance to the boundary of the neighborhood) as the N -th largest distance of d i .

To find the vectors a j , diffuse approximation uses least squares to minimize the following function J:

J(a 1 , a 2 ) = 1 2 N n=1 w(d n )   2 j=1 λ n j -p( θ n ) T a j 2   .
This results in

a j = P T W P -1 P T W L j ,
where P is a N × 3 matrix containing the vectors p of the N points included inside the neighborhood; L j , for j = 1, 2, are two vectors containing the N values of λ j of the points in the neighborhood; and W is a N × N diagonal matrix with the values of the weights associated to each point in the neighborhood:

P =      p(θ 1 ) T p(θ 2 ) T . . . p(θ N ) T      , L j =      λ 1 j λ 2 j . . . λ N j      , W =      w 1 0 • • • 0 0 w 2 • • • 0 . . . . . . . . . . . . 0 0 • • • w N     
.

Once the vectors a 1 and a 2 are known, θ can be computed by θ = A † X, where

X = λ 1 -a 1 0 λ 2 -a 2 0 , A = a 1 1 a 1 2 a 2 1 a 2 2
and A † is the Moore-Penrose pseudoinverse of A.

Interpolation

The diffuse approximation allows us to estimate the values of Ca and a/ for any arbitrary point λ / ∈ L but the quantity v 0 /U remains unknown. To estimate it, we apply a Delaunay triangulation on S T and identify the triangle corresponding to θ by projecting it onto S T . The velocity ratio v 0 /U is obtained by doing the weighted average of the values of v 0 /U at the three vertices of the triangle [START_REF] Amidror | Scattered data interpolation methods for electronic imaging systems: a survey[END_REF]. The weights are the ratio between the area of the subtriangle formed by the projected point and two vertices of the triangle and the area of the entire triangle.

Results

Validation of the method for an ovalbumin capsule

By way of illustration, we estimate the values of Ca, a/ and v o /U for the ovalbumin microcapsule depicted in the middle of Fig. 3a. The input geometrical quantities required by the method are the ones measured using the software ImageJ: L z / = 2.14 and L a / = 1.81. The resulting output values provided by the inverse analysis method are Ca = 0.082, a/ = 0.96 and v o /U = 1.29. Since this case was not part of the database, we deduce the corresponding numerical contour by weight-averaging the contours of the N = 14 neighbors. The superposition of the experimental image with the estimated numerical contour is shown Fig. 3b. The very good qualitative correspondence of the measured and predicted capsule profiles is consolidated by the mean distance between both sets of points (i.e. the Hausdorff Distance normalized by a), which presently is 0.066. This validates the use of the diffuse approximation method for mechanical identification.

Error estimation in the entire parameter space

An algorithm has been designed to assess the accuracy of the solutions θ provided by the method. A series of M test sets L * i , for i = 1, . . . , 137, has been generated in such a way that L * i = L -{λ i }. For each test set L * i , we thus remove a point λ i that emulates an experimental result. By applying the described method, θ = (Ca, a/ , v o /U ) is obtained. It is expected to have the same value as θ i ∈ T . The relative errors between θ and θ i are computed as

ε i j = θ j -θ i j θ i j , with j = 1, 2, 3.
An overview of the resulting relative errors is provided for each parameter in Fig. 11 generally higher along the borders of the domain than in the central region, especially for Ca. Previous studies showed that the identification method is only robust for sufficiently deformed capsules (10; 20). They based the criterion of reliability of the method on a global capsule stretch ratio Λ = P/2πa, P being the perimeter of the deformed capsule profile and 2πa the capsule perimeter at rest. They choose Λ > 1.04 as criterion (dashed black line in Fig 11).

If we only consider the cases that respect the criterion, we find mean relative errors equal to ε1 = 2.7% ± 4.1% for Ca, ε2 = 0.2% ± 0.1% for a/l, and ε3 = 0.2% ± 0.2% for v o /U (despite the notations, one must note that the errors cannot be negative). We thus find that the errors are ten times smaller on a/ and v o /U than on Ca.

Discussion

The high correspondence between the capsule contour measured experimentally and that identified from the numerical simulation using diffuse approximation (e. g. Fig. 3b) indicates that it is a very efficient technique to identify the mechanical properties of micrometric deformable capsules.

The mean error values indicate that the method is able to retrieve the unknown values of the microcapsule size a (from a/l) and mean flow velocity U (from v o /U ) with a precision well below 1%. As for the value of the surface shear modulus G S of the very thin microcapsule membrane, it is determined with a precision below 3%, which is remarkable for such small objects. The final precision on the determination of G S will additionally depend on the precision of the measurement of the viscosity µ of the suspending fluid, which is likely to be within a few percent [START_REF] Gubspun | Characterization of the mechanical properties of cross-linked serum albumin microcapsules: effect of size and protein concentration[END_REF].

The present results provide very interesting insight on the limit of the microchannel identification method. They show that the reliability criterion based on the global capsule stretch ratio Λ is very relevant. The advantage is that Λ is a quantity that can be determined from the images acquired experimentally and can thus provide an indication on the level of deformation of the microcapsule membrane. The limiting value was defined as Λ = 1.03 for Hu et al. [START_REF] Hu | Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: Effects of the membrane constitutive law[END_REF], which was corrected to Λ = 1.04 by Gubspun, Gires et al [START_REF] Gubspun | Characterization of the mechanical properties of cross-linked serum albumin microcapsules: effect of size and protein concentration[END_REF]. Fig. 11, on which the lines Λ = 1.04 have been added for indication, shows that a good accuracy is reached even for confinement ratios 0.70 ≤ a/l ≤ 0.85. No such results were obtained in the previous studies, because the microcapsules are too little deformed in the range. The diffuse approximation method thus allows to greatly extend the domain of validity of identification.

There is only one zone where the identification method leads to high errors even though the criterion is satisfied: a/ ≥ 1.1 and Ca ≤ 0.03. It is firstly caused by the intrinsic very low value of the capillary number in this region: small variations in the estimation of Ca lead to greater relative errors, especially in the Ca-range [0.005, 0.04]. Another cause is the abrupt changes in capsule deformed shapes that may happen for small increments of Ca when it is smaller than 0.02. Indeed, the capsule may not have a parachute shape (L p = 0) for the very small values of Ca. The large elliptical neighborhood (with N = 14) thus contains the two kinds of deformed capsule profiles, some with a parachute and others without, which greatly impairs the identification precision.

When compared to previously developed inverse analysis procedures based on microfluidics (9; 10), much lower errors are currently found with the diffuse approximation technique. As soon as the capsule is sufficiently deformed, the capsule size and surface shear modulus are determined with an error of only 0.2% and 2.7%, respectively. Hu et al. [START_REF] Hu | Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: Effects of the membrane constitutive law[END_REF] detemined these quantities with an error of 2-3% and 25% in the best cases. Similar precision on the determination of mechanical properties was found using micropipette aspiration. Zhelev et al. [START_REF] Zhelev | A novel micropipet method for measuring the bending modulus of vesicle membranes[END_REF], for instance, estimated the error to be within 25%. Using diffuse approximation for identification thus improves both the accuracy and reliability of the results.

The present results have been obtained for the neo-Hookean law, since we were interested in applying the technique to characterize the mechanical properties of ovalbumin capsules. The method is, however, valid regardless of the constitutive law used and could be applied to any artificial or natural (micro)capsule. The only challenge to use it on cells such as the red blood cells is purely experimental: the cells will indeed have to be flowed in a microchannel of about 10 microns. The results will have to be analyzed using the numerical database obtained for the Skalak's law [START_REF] Hu | Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: Effects of the membrane constitutive law[END_REF], which has been shown to well model their membrane deformation [START_REF] Skalak | Strain energy function of red blood cell membranes[END_REF].

Conclusion

We have presented a novel inverse analysis procedure that uses a data-driven diffuse approximation technique to identify the mechanical properties of microcapsule populations. This procedure is applied to the flow of a capsule through a long prismatic microfluidic channel of comparable size. The hydrodynamic forces inside the channel lead to the deformation of the membrane of the capsule, which eventually reaches a steady-state shape. The latter depends on the constitutive law of the membrane and two independent parameters: the capillary number Ca and the size ratio a/ . Geometrical quantities characterizing the capsule deformed profiles at steady state are determined from the images acquired experimentally using a rapid camera mounted on a microscope.

The identification method is based on the results of numerical simulations of the fluid-structure interactions between the capsule wall and the fluid flows, obtained offline. A comprehensive database of microcapsule deformed profiles and velocity ratios v o /U has been generated with the BI-FE numerical model described in [START_REF] Hu | Flow of a spherical capsule in a pore with circular or square cross-section[END_REF] for different values of Ca and a/ . Diffuse approximation uses this database to efficiently estimate the unknown values of Ca, a/ and v o /U of each capsule from its characteristic geometrical quantities measured experimentally. Low errors are achieved over a wide range of values of the estimated parameters, which indicates that the method allows to determine the surface shear modulus G S of the microcapsule membrane with a precision below 3%. It opens interesting perspectives for industrial applications that rely on microcapsules to transport active material, and require a tight control of the capsule mechanical properties to secure the targeted delivery.

Figure 1 .

 1 Figure 1. Initial configuration of a spherical capsule of radius a in a square-section microchannel of side 2 . Longitudinal and cross-sectional views.

Figure 2 .

 2 Figure 2. Numerical simulation of the evolution of a capsule, from rest to steady-state, as it flows along the microchannel.The capsule is shown for Ca = 0.12 and a/ = 0.9 at the non-dimensional times U t/ = 0 (a), 0.2 (b), 0.6 (c) and 2.4 (d).

Figure 3 .

 3 Figure 3. (a) Experimental images of ovalbumin microcapsules flowing at steady-state (10). (b) In red, their corresponding contours captured using ImageJ; in dashed blue, the contour identified by diffuse approximation: Ca = 0.064 and a/ = 1.02 (left); Ca = 0.082 and a/ = 0.96 (center); and Ca = 0.012 and a/ = 0.75 (right).

Figure 4 .

 4 Figure 4. Some geometrical quantities that can be measured from the capsule deformed profile: the maximum extension Lz along the z-axis, the axial length La and the parachute depth Lp = Lz -La (if any).

Figure 5 .

 5 Figure 5. Values of Ca and a/ included in the database. The domain where a steady-state capsule deformation exists is delimited by the black line in the case of capsules following the neo-Hookean constitutive law (21).

Figure 6 .

 6 Figure 6. Values of vo/U as a function of Ca and a/ .

Figure 7 .

 7 Figure 7. Points of T in the θ-space conforming the surface ST .

Figure 8 .

 8 Figure 8. a. View of the points of L in the λ-space: they lie on a narrow, elongated and tilted surface SL. b.To ease the application of the diffuse approximation technique, we apply a rotation of -45°around the axis perpendicular to the plane defined by L and centered on (0,0). Lz/ and La/ thus become L z / and L a / .

Figure 9 .

 9 Figure 9. Region of the λ -space showing an arbitrary point λ / ∈ L and its elliptical neighborhood, which includes N = 14 points λ i ∈ L .

Figure 10 .

 10 Figure 10. Weight function w(d).

Figure 11 .

 11 Figure 11. Heat maps of the relative errors ε, as a function of Ca and a/ , when estimating (a) Ca, (b) a/ and (c) vo/U . The region to the left of the dashed black line indicates capsule stretch ratios Λ ≤ 1.04.

Prepared using sagej.cls [Version: 2017/01/17 v1.20]

Prepared using sagej.cls

Acknowledgements

This work was supported by the Labex MS2T through the program "Investments for the future" funded by the French Government and managed by the National Agency for Research (Reference ANR-11-IDEX-0004-02). This project also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No. ERC-2017-COG -MultiphysMicroCaps)".

Conflicts of Interest

The authors certify that they have no conflict of interest.