Camille Tron
email: camille.tron@chu-rennes.fr

Michel Rayar

Antoine Petitcollin

Jean-Marie Beaurepaire

Caterina Cusumano

Marie-Clémence Verdier

Pauline Houssel-Debry

Christophe Camus

Karim Boudjema

Eric Bellissant

Florian Lemaitre

A high performance liquid chromatography tandem mass spectrometry for the quantification of tacrolimus in human bile in liver transplant recipients

Keywords: tacrolimus, high performance liquid chromatography, mass spectrometry, bile, alternative matrix, therapeutic drug monitoring

A high performance liquid chromatography tandem mass spectrometry for the quantification of tacrolimus in human bile in liver transplant recipients

Introduction

Long-term survival following liver transplantation has slowly evolved during the last five years. The rate of acute graft rejection (ACR) also remained stable with a frequency of about 8-15% at one year despite effective immunosuppression [START_REF] Wallemacq | Opportunities to optimize tacrolimus therapy in solid organ transplantation: report of the European consensus conference[END_REF]. Cornerstone of allograft rejection prevention, tacrolimus prevents the immune response against the graft by inhibiting interleukin-2 production by lymphocyte T cells [START_REF] Thomson | Mode of action of tacrolimus (FK506): molecular and cellular mechanisms[END_REF]. The drug presents highly variable pharmacokinetics and narrow therapeutic range making challenging the achievement of the balance between therapeutic efficacy and occurrence of side effects [START_REF] Venkataramanan | Clinical pharmacokinetics of tacrolimus[END_REF]. Therapeutic drug monitoring (TDM) of tacrolimus levels in whole-blood contributed to decrease the risk of ACR as well as the onset of adverse reaction [START_REF] Touw | Cost-Effectiveness of Therapeutic Drug Monitoring Committee of the International Association for Therapeutic Drug Monitoring and Clinical Toxicology, Costeffectiveness of therapeutic drug monitoring: a systematic review[END_REF]. However, some patients exhibit ACR while having blood levels within the recommended therapeutic range. This suggests that tacrolimus trough whole-blood concentrations imperfectly reflect tacrolimus concentrations at the effect site. Thus, looking for novel approaches of immunosuppressive drugs monitoring is needed to better prevent ACR.

In a prospective study in liver transplant recipients, Capron et al. [START_REF] Capron | Correlation of tacrolimus levels in peripheral blood mononuclear cells with histological staging of rejection after liver transplantation: preliminary results of a prospective study: PBMCs tacrolimus levels and graft rejection[END_REF] demonstrated the lack of correlation between tacrolimus trough whole-blood concentrations and the score of graft rejection, whereas tacrolimus intra-hepatic and peripheral blood mononuclear cells (PBMC) concentrations correlated well with incidence and intensity of histologically proved ACR. This work suggested that measuring tacrolimus concentrations in liver biopsy or in PBMC could better predict clinical outcomes.

The relevance of the determination of immunosuppressive drug concentration in the transplanted organ was also highlighted by Staatz et al. [START_REF] Staatz | Clinical pharmacokinetics and pharmacodynamics of tacrolimus in solid organ transplantation[END_REF]. However, such approaches of tacrolimus quantification are either invasive or expensive and the analytical workflow might be difficult to implement in daily clinical and laboratory practice [START_REF] Touw | Cost-Effectiveness of Therapeutic Drug Monitoring Committee of the International Association for Therapeutic Drug Monitoring and Clinical Toxicology, Costeffectiveness of therapeutic drug monitoring: a systematic review[END_REF]. We hypothesized that tacrolimus concentration in bile could be a surrogate marker of tacrolimus intra-hepatic concentration. The measurement of tacrolimus in bile appears cost-effective and suitable with clinical practice when T-tube biliary drainage is inserted in patients during surgery. Tacrolimus biliary concentration could reflect the free and non-metabolized fraction of the drug available at the target organ which is responsible for its pharmacological effect. Besides, tacrolimus is extensively metabolized by the liver and biliary excretion is thought to be the major route of elimination of its metabolites [START_REF] Iwasaki | Metabolism of tacrolimus (FK506) and recent topics in clinical pharmacokinetics[END_REF]. Polymorphisms in genes involved in this metabolism are a major cause of treatment response variability between patients [START_REF] Staatz | Clinical pharmacokinetics and pharmacodynamics of tacrolimus in solid organ transplantation[END_REF]. Thus, tacrolimus concentration in bile could directly depend on the magnitude of drug metabolism, leading to provide valuable information about its pharmacokinetics. Studies reporting tacrolimus determination in bile are sparse and were published a few decades ago [START_REF] Shimomura | Required transient dose escalation of tacrolimus in living-donor liver transplant recipients with high concentrations of a minor metabolite M-II in bile[END_REF][START_REF] Firdaous | Excretion of tacrolimus glucuronides in human bile[END_REF][START_REF] Christians | High performance liquid chromatography/mass spectrometry of FK 506 and its metabolites in blood, bile, and urine of liver grafted patients[END_REF]. They are mainly focused on investigating the drug metabolic pathway without any extensive description of the analytical validation which is unfortunate because this matrix is known to be associated with several bioanalytical challenges [START_REF] Srinivas | An overview of various validated HPLC and LC-MS/MS methods for quantitation of drugs in bile: challenges and considerations[END_REF]. Bile is an unconventional alternative matrix for TDM and demonstration of the reliability of the analysis is a critical step before any clinical application. Thus, prior to investigating whether biliary tacrolimus concentration could be a good marker of its immunosuppressive activity, we aimed at developing and validating, according to international guidelines [START_REF]Guideline on bioanalytical method validation[END_REF], a high performance liquid chromatographytandem mass spectrometry (HPLC-MS/MS) method for the determination of tacrolimus in bile from liver transplant recipients. The analytical method was then applied to analyze bile samples from liver transplant recipients.

Material and methods

Chemicals and material

Tacrolimus was purchased from LGC standards (Folsheim, France). Ascomycin was purchased from Sigma-Aldrich (Saint-Quentin, France). Methanol and acetonitrile of LC/MS grade were purchased from Carlo Erba Reagents (Val de Reuil, France). Ethyl acetate, methyl-ter-butyl ether (MTBE) and dichloromethane were obtained from VWR international (Fontenay sous Bois, France). Ammonium acetate, zinc sulfate heptahydrate and formic acid were obtained from Fisher Chemicals (Waltham, USA). Water was purified using a Milli-Q® Ultrapure Water System (Merck Millipore, Milford, MA, USA). Beta-glucuronidase enzymes from E. Coli (type IX-A), Helix pomatia and bovine liver origins were purchased from Sigma-Aldrich (Saint-Quentin, France). OASIS® HLB SPE 96-wells plate (30 mg) and OSTRO® 96-wells plates were purchased from Waters (Saint-Quentin, France).

Human bile was collected from the T-tube biliary drainage inserted in biliary anastomosis during the surgical procedure. Drug free human bile was collected before the onset of the immunosuppressive treatment. Drug-free bile samples from 7 individual liver transplant recipients were used to prepare a batch of pooled biles used in the validation and the clinical application analysis.

HPLC-MS/MS equipment and conditions

The chromatographic system (ThermoFisher, San Jose, CA, USA) included a Surveyor Autosampler and an HPLC Surveyor MS pump. A C18 Hypersil Gold column (50 x 2.1 mm, 3 μm) fitted with a guard column (10 x 2.1 mm, 3 μm) (Thermo Electron, Dreieich, Germany) was used and maintained at a constant temperature of 60 °C. The autosampler was set at 15°C during analysis. To measure tacrolimus in bile, gradient elution was performed with a mobile phase composed of a mixture of 0.1% formic acid and 2mM ammonium acetate in water (eluent A) or in acetonitrile (eluent B). A multistep gradient adapted from Dubbelboer et al. [START_REF] Dubbelboer | Quantification of tacrolimus and three demethylated metabolites in human whole blood using LC-ESI-MS/MS[END_REF] was used at a flow rate of 0.4 ml/min and was programmed as follows: equilibration at initial conditions with 40% of B, increase to 70% of B from 0 min to 0.1 min, increase to 75% of B from 0.1 min to 1.4 min, increase to 100% of B from 1.8 min to 2.45 min, stabilization at 100% of B from 2.45 min to 3.10 min, reversion to the starting conditions at 40% of B from 3.1 min to 3.15 min and re-equilibration with the initial composition from 3.15 min to 5.0 min. The total run time was 5.0 min.

The HPLC system was interfaced with a triple stage quadrupole mass spectrometer Finnigan™ TSQ ® Quantum Discovery Max (ThermoFisher, San Jose, CA, USA). Positive electrospray ionization interface parameters were as follows: spray voltage 4.5 kV, sheath gas and auxiliary gas (N2) 35 and 10 arbitrary units, respectively, capillary heater temperature 250°C. The MS run was performed in the multiple reaction monitoring (MRM) scanning mode. The adduct [M+NH4 + ] transitions m/z 821.42 m/z 768.53 (collision energy at 20 eV and Tube lens value at 135 V) and m/z 809.55 m/z 756.52

(collision energy at 27 eV and Tube lens value at 129 V) were monitored for tacrolimus and ascomycin, respectively. Data acquisition and analysis were performed using LCQuan software, version 2.5.6 (ThermoFisher, San Jose, CA, USA).

Preparation of standards (Std) and quality control (QC) samples

Two batches of stock solutions of tacrolimus were independently prepared in methanol at a concentration of 1000 ng/mL (one for QC and one for Std). A stock solution of ascomycin was prepared in acetonitrile at a concentration of 500 ng/mL. These stock solutions were stored at -80°C. Working solutions of each calibration Std and each QC level were daily prepared by dilution of the tacrolimus stock solution in methanol. A working solution of ascomycin used as internal standard (IS) was daily prepared in acetonitrile at the concentration of 250 ng/mL. Aliquots of 250 μL of drug-free human bile were spiked with corresponding working solutions to obtain 6 non zero calibrators levels at 0.5, 1, 1.5, 5, 10, 20 ng/mL and QC samples at 0.5 (Lower limit of quantification), 1.5 (Low), 10 (Medium) and 20 ng/mL (High). The percentage of organic solvent in bile was lower than 8%.

Sample preparation

An aliquot of 250 μL of bile was transferred into a 4 mL glass tube. IS was added (40 μL of ascomycin 250 ng/mL) and the sample was diluted with 800 μL of water and vortexed 3s. Then, precipitation was performed by adding 300 μL of a mixture of acetonitrile / zinc sulphate 0.05 M in water 1:1 v/v followed by a liquid/liquid extraction using 2 mL of ethyl acetate. Samples were gently mixed for 10 min and centrifuged at 3000 g for 10 min at 4°C. The supernatant was evaporated to dryness under nitrogen flow at room temperature. The sample was reconstituted with 500 μL of a mixture of water/acetonitrile 1:1 v/v, then 100 μL of ammonium sulphate 40% in water were added and 12 μL of the organic upper layer were injected in the LC-MS/MS system.

Method development and validation

Method development

In order to find the best procedure to extract tacrolimus from bile, several sample preparation conditions were investigated. Various mixtures of precipitant agents such as methanol, acetonitrile, zinc sulphate were tested. A pass through sample preparation plate was evaluated for phospholipids and proteins clean-up. Liquid-liquid extraction (LLE) was compared to solid phase extraction (SPE). Several solvents were compared for LLE among ethyl acetate, MTBE and dichloromethane. The optimal procedure was selected based on visual criteria, signal response and practical considerations.

Method validation

The analytical method was validated according to international guidelines from the European Medicines Agency on bioanalytical method validation [START_REF]Guideline on bioanalytical method validation[END_REF].

Selectivity, sensitivity

Selectivity was investigated using six independent sources of human bile. Each one was used to prepare blank samples and samples spiked with tacrolimus at the expected lower limit of quantification (LLOQ).

The lack of endogenous interferences was checked by thoroughly examining the chromatograms of blank samples in the retention window containing the peaks of the analyte or the IS. For each source of matrix, signal in blank should be less than 20% of the LLOQ area. The LLOQ was defined as the lowest amount of analyte in a sample determined with precision and accuracy within ±20%. Interferences coming from possible co-administered medications in liver transplants were evaluated for 46 drugs (see table 1). Because tacrolimus is extensively metabolized by the liver and transformed in oxidized and conjugated metabolites excreted in bile, potential interferences caused by co-eluted metabolites were investigated in samples from patient receiving tacrolimus.

Linearity

Method linearity was assessed by analyzing calibration samples spiked with the analyte at 6 concentration levels. Calibration standards analysis was performed over three different days.

Calibration curves were established by plotting the peak area ratio of the target compounds to the IS versus the nominal concentrations. The homoscedasticity assumption for linear regression analysis was tested using the F-test. A minimum of 75% of the standard calibration samples had to be in the ±15% range (LLOQ: ±20%) of the nominal value.

Accuracy and precision

Accuracy and precision were determined by replicate analysis of samples containing known amounts of tacrolimus daily prepared at each concentration level (LLOQ, Low, Medium, High). Within-day accuracy and precision were determined by analyzing QCs in five replicates in a single validation batch.

Between-day accuracy and precision were determined by repeating analysis of five replicates over three different days. Precision was assessed by calculating the coefficient of variation (CV). Between-day precision data were compared using one-way ANOVA. Accuracy was reported as the relative error (RE) or bias to the theoretical value. The acceptance criteria for precision and accuracy were ±15% except for LLOQ which should not deviate more than 20%.

Carry over

Carry-over was evaluated by sequentially injecting an upper limit of quantification (ULOQ) sample (highest calibration standard) immediately followed by an extracted blank sample. The response in the blank matrix injection at the retention time region of tacrolimus should be less than 20% of the mean response at the LLOQ.

Extraction recovery and matrix effect

Recovery and matrix effect were assessed for each QC level with the post extraction addition technique adapted from Matuszewski et al. [START_REF] Matuszewski | Strategies for the assessment of matrix effect in quantitative bioanalytical methods based on HPLC-MS/MS[END_REF]. QC samples were prepared by spiking drug-free bile from 6 different sources and were extracted according to the procedure described above (samples A). For each source, blank bile samples were extracted and post-fortified with tacrolimus and IS at the same concentrations than in the QC extracts (samples B). Neat solutions (samples C) were prepared in duplicate with the extraction solution spiked with tacrolimus and ascomycin at the same concentrations as in the extracts A and B. Recoveries were calculated as follow: recovery (%) = (peak area of sample A / peak area of sample B) x100. Absolute matrix effects of each source were estimated for tacrolimus and the IS by matrix factors (MF) determined as MF= (peak area of sample B / peak area of sample C) x100. IS corrected MF was calculated by dividing the MF of the tacrolimus by the MF of the IS. The CV of the IS-normalized MF calculated from the 6 lots of matrix should not be greater than 15 %.

Stability

Stability of tacrolimus in bile was assessed for samples prepared in blank bile from three different sources and fortified at QCs level concentrations and stored during 20 hours at room temperature. Longterm stability covering a 6 months period of storage at -80°C was also evaluated and after 3 freeze-thaw cycles at -80°C. Stability of the extract in the auto-sampler was assessed by re-injecting extracted calibration curve and QCs low, medium, high vials kept 24 hours at 15°C. Stability of tacrolimus stock solution in methanol stored at -80°C for 4 years was also studied. Stability was claimed if bias between tested condition and freshly prepared sample at the same concentration was no more than ±15%.

Besides, it is assumed that Tacrolimus-glucuronide metabolites are excreted in bile, so it was worth checking whether the glucuronide form could be reversely transformed in the parent molecule (nonmetabolized tacrolimus) by the glucuronidase enzymes found in bile. Thus, bile samples from 6 patients treated with tacrolimus were collected for 2 hours on ice to inhibit any enzymatic activities. Aliquots were withdrawn and incubated for 15 hours at room temperature or at 37°C with a mixture of betaglucuronisases in pH 5.0 acetate buffer (5000 UI/mL). The enzymes from three separate origins were used to ensure the best catalytic activity as possible. A control aliquot was immediately stored at -80°C after collection. Comparison of tacrolimus concentrations between each experimental condition allowed highlighting any overestimation of the bile concentration of the immunosuppressant due to a back-conversion of a metabolite into the parent drug during the period of bile collection at the patient bedside.

Clinical application

The LC-MS/MS method was applied after validation to two clinical applications. Bile was collected in recent liver transplant recipients and following the onset of twice daily tacrolimus treatment. First, tacrolimus biliary concentrations were measured in sequential fractions (0 to 2h, 2 to 4h, 4 to 6h and 6 to 10h after tacrolimus intake) of fresh bile. A total of 13 sequential data sets coming from 6 individual patients were collected. The objective was to explore the excretion profile of tacrolimus in bile after drug intake. A second application aimed at studying the correlation between whole-blood tacrolimus trough concentrations and tacrolimus biliary concentrations or biliary excretion rates over a 12-hour collection period at the patient bedside. This analysis was intended to reflect liver exposition to tacrolimus over a drug intake period. Whole-blood trough concentration is the parameter used routinely to monitor immunosuppressive treatment. EDTA blood samples were collected simultaneously to bile samples just before tacrolimus administration in 30 liver transplant recipients. Tacrolimus concentrations were determined in blood using an in-house validated HPLC-MS/MS method adapted from the literature [START_REF] Seger | A rapid HPLC-MS/MS method for the simultaneous quantification of cyclosporine A, tacrolimus, sirolimus and everolimus in human blood samples[END_REF]. Linear regression and Pearson's correlation coefficient were used to investigate the correlation between blood and bile parameters.

The exact volumes of bile excreted during each collection period were carefully monitored to be able to express results in amount of tacrolimus excreted during a given period of time. This allowed comparing results between patients independently from the biliary flow rate.

The study was part of a clinical trial approved by the local ethical committee (N°16.45) and has been declared on clinicaltrials.gov (NCT02820259).

3.

Results

Method development

The composition of bile is complex as it contains various elements such as water, electrolytes and a number of organic molecules such as bile acids, cholesterol, phospholipids and bilirubin. Consequently, a compromise had to be found between interfering compounds removal and analyte of interest recovery.

In order to clean up the extract, to minimize matrix effect and to obtain an acceptable peak shape, the sample preparation procedure was optimized. A step of precipitation was necessary to remove solid particles from the extract. A mixture of acetonitrile, zinc sulphate and water displayed good precipitant properties and partially avoided extraction of yellow biliary pigments compared to precipitation with an organic solvent alone (acetonitrile or methanol). SPE extraction using HLB plate or proteins and phospholipids removal with Ostro® plate led to cleaner extracts but were associated with lower tacrolimus recovery. Because tacrolimus is a lipophilic drug, analyte recovery was improved with LLE using an organic solvent. Ethyl acetate was chosen because it provided the best peak shape and a high recovery. Regarding practical aspects, ethyl acetate was also preferred to MTBE and dichloromethane because its viscosity allowed more accurate pipetting.

Validation

Selectivity, sensitivity

There were no interferences from either endogenous compounds or possible co-administered drugs at the retention times of tacrolimus and ascomycin (respectively 2.30 and 2.28 min) in human bile samples.

As a consequence of the high specificity of the tandem mass spectrometric detection, no baseline separation between analytes was necessary. Signal of noise peaks in blank samples were less than 20% of the areas of tacrolimus in spiked samples at the LLOQ concentration. However, when incurred patient samples were analyzed to look for metabolite interferences, a co-eluted peak appeared a few seconds before tacrolimus peak on the same MS/MS m/z transition than tacrolimus. Chromatographic resolution between these peaks was not good enough to quantify tacrolimus accurately. Consequently, liquid chromatography parameters had to be optimized using gradient elution (reported above) instead of isocratic elution (initially used during method development) to eliminate the interfering peak. It is assumed that this co-eluted peak comes from tacrolimus-glucuronide dissociation in the MS source.

Since glucuronide metabolite is more hydrophilic than the parent drug, it is eluted before it in reverse phase mode. This hypothesis was confirmed using beta-glucuronidases mixture to force glucuronide hydrolysis before extraction. Six incurred patient bile samples were incubated before extraction 15 hours at room temperature without beta-glucuronidase (condition A) or 15 hours at 37°C with a mixture of beta-glucuronidase in pH 5.0 buffer (condition B). In condition B, the metabolite was back converted to tacrolimus before extraction and only one peak appeared on tacrolimus chromatogram at the correct retention time (using isocratic elution). As expected, tacrolimus peak area was significantly higher in condition B than in condition A (tacrolimus response ratio mean increase ± SD = 7.2±3.1). A representative chromatogram is presented in Figure 1.

Linearity

The linearity of the method was obtained over the calibration range using linear regression. The best fit was obtained with a weighing factor of 1/x to achieve homoscedasticity. Back calculated concentrations of the calibration standards were within the acceptance criteria (±15% of the target concentration, except ±20% at the LLOQ) and the coefficient of correlation was > 0.99 for every validation analysis.

Slopes, intercepts and coefficient of determination mean values and standard-deviations were respectively as follow (n=3): 0.095±0.016, 0.008±0.012, 0.996±0.001.

Accuracy and precision

Results of within-day and between-day precision and accuracy determined at four concentrations are detailed in table 2. They fulfilled the acceptance criteria since bias and CV did not exceed 20% for LLOQ and 15% for other QC concentrations.

Carry over

No carry-over was observed in the validation experiments as the responses of the blank sample after the injection of an ULOQ sample were less than 20% of the response of the LLOQ samples.

Extraction recovery and matrix effect

Recoveries were high and close to 95% for tacrolimus and ascomycin at low and high concentrations.

Matrix effects determined from 6 different sources are presented in table 3. A significant absolute matrix effect due to ion enhancement was observed. There was also a relative matrix effect close to 20% within the concentration range. However, matrix effect was totally corrected by the IS (ascomycin) since mean corrected matrix factors were close to 1 and variation among samples from different sources were less than 15% at each concentration level, which is defined to be acceptable by the guidelines [START_REF]Guideline on bioanalytical method validation[END_REF].

Stability

As shown in table 4, at room temperature, tacrolimus was stable in bile for 20 hours. This is relevant for clinical applications because stability should cover the time range from the collection at the patient bedside (about 12 hours) to the sample transport to the laboratory. No drug loss was observed after 6 months of storage at -80°C, neither after 3 freeze and thaw cycles. Extracts were found stable in an auto-sampler set at 15°C for 24 hours. There was no decrease in tacrolimus stock solution concentration stored 4 years at -80°C. Bile storage at room temperature for 15 hours (to mimic pre-analytic conditions) did not result in back transformation of tacrolimus-glucuronide metabolite in tacrolimus meaning that no hydrolysis occurred during bile collection at patient bedside. Tacrolimus concentration should not be overestimated because of beta-glucuronisase enzymes present in bile. Nevertheless, sample incubation with a cocktail of beta-glucuronidases in optimal catalytic conditions confirmed the relevance of this concern because tacrolimus-glucuronide was able to be directly back-transformed in tacrolimus after hydrolysis increasing in a very large extend tacrolimus signal compared to a control sample.

Clinical application

The method was successfully applied to the analysis of bile in patient samples. Representative ion chromatograms of tacrolimus of a blank sample (A), a sample spiked at the LLOQ (B) and a patient sample (C) are shown in figure 2. Measurement of tacrolimus concentrations in bile in sequential fractions allowed calculating tacrolimus amounts and tacrolimus excretion rates for the corresponding collection period. Tacrolimus mean excretion rate was (mean±SD) 25.4±17.4 ng/h during the first 2 hours following drug intake and decreased slowly over the day to 14.0±7.7 ng/h 10 hours after drug administration. Results are reported in table 5. Mean tacrolimus excretion profile in bile is represented in figure 3A as a mean excretion rate over time, and in figure B as mean cumulative amount over time.

The second clinical application aimed at evaluating correlation between whole-blood tacrolimus concentrations and tacrolimus bile concentrations or tacrolimus bile amounts. Mean tacrolimus concentration in bile collected in 30 liver transplant recipients was 1.1±0.6 ng/mL. This value was reported to the volume of bile produced over 12 hours and the mean amount of tacrolimus found in the bile collection was 192±122 ng. Mean biliary tacrolimus excretion rate on 12 hours was 16.0±10.2 ng/h. No correlation was found between the amount of tacrolimus excreted in bile over the 12-hour period between two drug intakes and tacrolimus trough concentration in whole blood (p= 0.88). Moreover, no correlation was found between the concentration of tacrolimus measured in bile collected over the 12hour period between two drug intakes and tacrolimus trough concentration in whole blood (p= 0.16) (figure 4A and4B).

Discussion

To the best of our knowledge, this is the first extensive report of a LC-MS/MS method aiming at quantitating tacrolimus in bile. Two teams also developed an analytical method to measure tacrolimus in bile using chromatographic separation [START_REF] Firdaous | Excretion of tacrolimus glucuronides in human bile[END_REF][START_REF] Christians | High performance liquid chromatography/mass spectrometry of FK 506 and its metabolites in blood, bile, and urine of liver grafted patients[END_REF]. These studies were conducted some decades ago with ancient instruments less sensitive and less specific than now days. For instance, Firdaous et al. used a HPLC method coupled with an immune-enzymatic detection which is not the actual gold-standard for immunosuppressive drugs quantitation [START_REF] Firdaous | Excretion of tacrolimus glucuronides in human bile[END_REF]. Indeed, immunological techniques can lead to crossreactivity between tacrolimus and its metabolites which may cause a unacceptable positive bias in the measurement [START_REF] Seger | Assuring the Proper Analytical Performance of Measurement Procedures for Immunosuppressive Drug Concentrations in Clinical Practice: Recommendations of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology Immunosuppressive Drug Scientific Committee[END_REF]. Shimomura et al. measured tacrolimus and three of its main metabolites in bile using an LC-MS/MS system [START_REF] Shimomura | Required transient dose escalation of tacrolimus in living-donor liver transplant recipients with high concentrations of a minor metabolite M-II in bile[END_REF]. However, nothing was reported about the analytical method performances.

In liver transplant patients, the relationship between tacrolimus efficacy and intracellular or tissue (hepatic biopsy) concentrations of the drug has been reported to be closer than with whole-blood concentrations [START_REF] Capron | Correlation of tacrolimus levels in peripheral blood mononuclear cells with histological staging of rejection after liver transplantation: preliminary results of a prospective study: PBMCs tacrolimus levels and graft rejection[END_REF]. This is not surprising because the intracellular fraction of the drug is the fraction available at the site of action and tissue fraction represents the local concentration of the drug in the targeted graft. Both of these fractions could also be better related to tacrolimus free fraction (i.e. the active fraction of the drug). Thus, monitoring intracellular or tissue tacrolimus concentrations appears to be of better relevance than monitoring whole-blood concentrations. Unfortunately, measuring intracellular concentrations is time-consuming, expensive and requires expertise which is only available in few centers. In the same way, measuring tissue concentrations requires time and money and can only be conducted on hepatic biopsy which is an invasive procedure. Facing these difficulties, we have developed a method to measure tacrolimus in bile. Indeed, tacrolimus concentrations in bile could reflect at the same time the local concentration of the drug, as bile is a direct product of hepatocytes efflux, and the free-fraction of the drug, as tacrolimus is freely eliminated through biliary secretion.

During the early post-operative period, bile produced by the liver graft could be easily collected when a biliary drainage is left in the biliary tract. It is intended to prevent early biliary leakage and stricture by reducing intra-ductal pressure [START_REF] Wojcicki | Biliary Tract Complications after Liver Transplantation: A Review[END_REF] as well as to confirm bile production which is considered as a good marker of graft function. It then allows to easily access to the bile and tacrolimus concentration can be measured in it.

Measuring drugs concentrations in bile appears to be challenging. Bile is a complex matrix containing bile acids, phospholipids and bilirubin. Ensuring appropriate selectivity of the method can be a complex process and involves: obtaining sufficient extraction process, assessing drug stability in the matrix, ensuring adequate chromatographic separation, avoiding matrix effect and ensuring lack of influence of potential in-source dissociation of glucuronide into the parent drug.

More than 95% of tacrolimus is excreted in bile almost exclusively as metabolites [START_REF] Möller | The disposition of 14C-labeled tacrolimus after intravenous and oral administration in healthy human subjects[END_REF]. As a result, limited quantity of unchanged drug is eliminated in bile and the sensitivity of the method is crucial. The sample preparation of the present method with its high extraction process allowed reaching a lower limit of quantification of 0.5 ng/mL. This limit has been shown to be sufficient when the method was applied to clinical samples. Even if the drug is mainly metabolized through phase I mechanisms leading to demethylated and hydroxylated metabolites [START_REF] Iwasaki | Metabolism of tacrolimus (FK506) and recent topics in clinical pharmacokinetics[END_REF][START_REF] Sattler | Cytochrome P-450 3A enzymes are responsible for biotransformation of FK506 and rapamycin in man and rat[END_REF][START_REF] Wallemacq | FK506 (tacrolimus), a novel immunosuppressant in organ transplantation: clinical, biomedical, and analytical aspects[END_REF], part of tacrolimus is directly conjugated via UDP-glucuronyltransferase (UGT) 1A4 [START_REF] Laverdiere | In Vitro Investigation of Human UDP-Glucuronosyltransferase Isoforms Responsible for Tacrolimus Glucuronidation: Predominant Contribution of UGT1A4[END_REF]. This tacrolimus-glucuronide might be hydrolyzed in bile during collection and/or storage. This phenomenon was explored as it could result in overestimation of drug concentration. Particularly, there was no difference between tacrolimus measured in bile patients collected on ice (in order to inhibit glucuronidase activity) and assayed immediately or after 15 hours at room temperature. Then, we demonstrated that no back-conversion of the glucuronide metabolite occurred during the pre-analytical steps. Degradation of the unchanged drug within the matrix was also investigated. In the present work, we ensured drug stability during collection for 12 hours as well as short-term and long term stability under various conditions of temperature. As presented earlier in this manuscript, in-source dissociation of tacrolimus-glucuronide was a cause of concern during method development. Such a phenomenon has already been described for other directly conjugated drugs [START_REF] Mess | A practical approach to reduce interference due to in-source collision-induced dissociation of acylglucuronides in LC-MS/MS[END_REF][START_REF] Vogeser | Potential lack of specificity using electrospray tandemmass spectrometry for the analysis of mycophenolic acid in serum[END_REF]. In the first steps of the method development, a duplication in patients' tacrolimus chromatographic peaks appeared. We put forth the hypothesis that this duplication was due to tacrolimus-glucuronide dissociated within the ionization source with the metabolite being eluted earlier than the parent compound. Adding a glucuronidase enzymes cocktail to the bile of transplant recipients collected on ice resulted in an increase in tacrolimus concentrations and in the disappearance of the peak with the shorter retention time. This confirmed that a part of tacrolimus is directly conjugated via UGT, as demonstrated by Laverdière et al., and that in-source dissociation of tacrolimus-glucuronide into unchanged tacrolimus has to be clearly assessed to avoid the risk of overestimation of biliary tacrolimus concentration. Modifying chromatographic gradient allowed us separating tacrolimus from its metabolites. It highlighted the relevance of the analysis of incurred patient samples in the early steps of the validation procedure and how selectivity issue might be a critical point when analyzing such a complex matrix.

The present fully validated LC-MS/MS method was applied to two clinical applications. First, we measured biliary tacrolimus concentrations in sequential fractions (0 to 2h, 2 to 4h, 4 to 6h and 6 to 10h post drug intake) of fresh bile collected in recently liver transplant recipients. Despite high interindividual variability, this clinical application provided interesting information. Tacrolimus appeared to be excreted to a greater extent during the first two hours post-dose administration. Tacrolimus elimination can thereby be studied using this novel LC-MS/MS method.

Finally, we have determined tacrolimus concentrations in bile collected during 12 hours and investigated the relationship between, tacrolimus amount excreted in bile or tacrolimus concentration in bile, and tacrolimus concentration in whole-blood in 30 liver transplant recipients. No correlation was found between tacrolimus excreted through 12-hours bile secretion and the trough whole-blood concentration of the drug. As tacrolimus concentration in bile could better reflect local and unbound concentration of the drug, and because it does not appear to be correlated with whole-blood concentration, this concentration might be more closely related to the immunosuppressive effect of the drug. This hypothesis have to be confirmed by showing a significant correlation between tacrolimus concentration in bile and tacrolimus concentration within PBMC which is recognized as a good marker of the drug immunosuppressive activity. Our team is currently performing this study (STABILE study, clinical trial: NCT02820259). The measurement of tacrolimus concentration in bile should therefore be further evaluated as a potential way of monitoring the drug effect. The present method should then be applied to evaluate the value of such a biomarker in monitoring treatments in liver transplant recipients.

Of course, there are limitations in the usefulness of this LC-MS/MS method. First, this method is only effective when a biliary drainage is present, which is not a consensual approach. However, in our center, we think that this method is relevant especially when considering the use of graft from extended criteria donor and is therefore systematically performed. Then, as T-tube drain is usually clamped between 7 to 10 post-operative days, monitoring of tacrolimus in bile is only possible thorough the early postoperative period. However, the first week after transplantation is the most critical and difficult period in management of transplanted patients. Indeed, the progressive liver function recovery has a major impact on the pharmacokinetics of immunosuppressive drugs which is not taken in consideration by blood dosage of tacrolimus, resulting in difficulty in dose adjustment during this period. Therefore, occurrence of ACR and adverse effects related to tacrolimus could be more prevalent during the first post-operative days requiring maybe a therapeutic drug monitoring of better performance than blood dosage of tacrolimus can offer.

Conclusion

An HPLC-MS/MS method has been thoroughly validated for the quantification of tacrolimus in bile.

An extraction process based on protein precipitation and liquid-liquid extraction leads to high recovery and good analytical performances since the assay fulfilled acceptance criteria of international guidelines.

The method was successfully applied to the quantification of tacrolimus in bile from liver transplant recipients. It allowed getting preliminary data about tacrolimus excretion profile in bile and the lack of correlation between tacrolimus whole blood concentration and tacrolimus liver exposition. Thus, this alternative and innovative analytical approach of tacrolimus bio-analysis appears suitable for further studies evaluating biliary tacrolimus concentration as a new pharmacological marker of immunosuppressive activity.

Conflict of interest statement

Florian

  Lemaitre received a research grant from Astellas Pharma and has received speaker fees from Chiesi SA Funding: The study was partially funded by the COmité de la REcherche Clinique Translationnelle (CORECT) of the Rennes University Hospital.

Figure 1 :

 1 Figure 1: Representative LC-MS/MS chromatograms of tacrolimus (for tacrolimus m/z MS/MS transition)analysed in an incurred patient bile sample. An un-resolved peak, coming from a metabolite back conversion to tacrolimus in the MS system source, was eluted with tacrolimus in sample incubated 15 h at room temperature (FigureA). After hydrolysis before extraction (15 h at 37°C, pH5) with a cocktail of beta-glucuronidases, the metabolite was extensively converted to tacrolimus and only a single peak of higher area was detected by the MS system (FigureB). Signals absolute intensities are reported as area under the curve next to corresponding peaks.

Figure 2 :

 2 Figure 2: Representative LC-MS/MS chromatograms of tacrolimus analysed in a blank sample (A), a sample spiked at the LLOQ (B) and a patient sample (C). The first peak in the patient sample (retention time 1.5 min) comes from the glucuronide dissociation in the LCMS system.

Figure 3 :

 3 Figure 3: Excretion profile of tacrolimus in bile. Excretion rate according to the collection period post tacrolimus administration (mean±SD, n=13, Figure A). Cumulated amount of tacrolimus excreted in bile along the sequential collection (black histograms) and total excretion during the previous 12 h (grey histogram) (mean±SD, n=13, Figure B).

Figure 4 : 19 (

 419 Figure 4: Correlation plots between tacrolimus trough concentrations in whole blood and tacrolimus amount (Figure A, p=0.88) or tacrolimus concentration (Figure B, p=0.16) measured in bile of liver transplant patients (12-hour collection). Trend curves and their respective equations and coefficients of determination are reported

Table 5 :

 5 Quantitative parameters measured in sequential fractions of fresh bile

		3	10.3	3.7
	QC2	4.5	2.5	-6.5
	QC3	2.4	-1.3	-7.9
	QC4	2.3	-3.2	-8.8
	Incurred patient bile sample incubated 15h at Room Temperature (bias 2 %) (n=6)	Incurred patient bile sample incubated under forced hydrolysis 15h at 37°C with beta-glucuronidase cocktail (bias 2 %) (n=6)
	-10.9		519.9

1

Bias compared to QCs freshly prepared

2

Bias compared to control sample collected on ice to inactivate enzymatic activity and immediately stored at -80°C 24

Acknowledgements 13

The study was partially funded by the COmité de la REcherche Clinique Translationnelle (CORECT) of the Rennes university hospital.


Jean-Baptiste Masson
email: jean-baptiste.masson@polytechnique.edu

Guilhem Gallot
email: guilhem.gallot@polytechnique.edu

Extra energy coupling through subwavelength hole arrays via stochastic resonance

Keywords: numbers: 73.20.Mf, 05.40.Ca, 41.20.Jb

Interaction between metal surface waves and periodic geometry of subwavelength structures is at the core of the recent but crucial renewal of interest in plasmonics 1,2,3,4 . One of the most intriguing points is the observation of abnormal strong transmission through these periodic structures, which can exceed by orders of magnitude the classical transmission given by the filling factor of the plate 3 . The actual paradigm is that this abnormal transmission arises from the periodicity, and then that such high transmission should disappear in random geometries. Here, we show that extra energy can be coupled through the subwavelength structure by adding a controlled quantity of noise to the position of the apertures. This result can be modelled in the statistical framework of stochastic resonance.

The evolution of the coupled energy with respect to noise gives access to the extra energy coupled at the surface of the subwavelength array.

We investigated the transmission of subwavelength arrays with a controlled quantity of noise added to the position of the subwavelength apertures, in order to study how plasmonic properties would disappear with addition of noise. Most surprisingly, our experimental results demonstrate a strong increase of coupled energy through the array by adding a small quantity of noise to the lattice. This unexpected extra energy coupling could not be modelled using standard plasmonic theories 5,6,7,8 , such as Bethe, Bloch waves or CDEW models, since they intrinsically predict maximum energy coupling with perfectly periodic organization. We explain our results using stochastic resonance theory 9 , which describes how a system can be optimized by the presence of a certain amount of noise. Furthermore, the evolution of the coupled energy for relatively large values of noise gives access to fundamental characteristics of the establishment of the electromagnetic propagation and coupling at the surface. It allows the direct measurement of the extra energy coupled at the surface of the screen originating from the creation of the abnormal high transmission process.

Experiments were made in the terahertz domain since this domain is particularly suited for this study thanks to the lack of plasma resonance on metals in this part of the electromagnetic spectrum, and to the high precision achievable in the screen design. We designed noised arrays of squared subwavelength apertures by adding Gaussian noise displacements to the hole centres with a standard deviation σ (see Fig. 1). No deviation (σ = 0) corresponds to perfectly periodic structure, while high deviations deal with fully random aperture positions. Numerous plates have been investigated, one for each noise deviation. Three typical experimental spectra are shown in Fig. 2. For perfectly periodic arrays (σ = 0), the spec-trum exhibits the usual strong asymmetrical first resonance and a second resonance scaling as √ 2. For large deviations (σ = 60 ± 0.5 µm), spectra show a less intense, much wider and symmetrical resonance, and no clear shapes for higher frequencies. For low quantity of noise, a much unexpected behaviour is observed for a small amount of noise (σ = 15.4 ± 0.5 µm).

Here, the spectrum exhibits a much stronger resonance. This resonance is still asymmetrical, and the complete spectrum exhibits all usual Surface Plasmon Polaritons (SPPs) features, but more energy is coupled through the array. This result is clearly unexpected, and seems to indicate that noise added to the structure increases the coupled energy. To explain these results, the evolution of transmitted spectrum with the amount of noise has been studied. To reduce the influence of spectrum artefacts due to specific patterns generated on the noised arrays, we introduce the transmission of the array T = E t /E 0 , where E t and E 0 are the total transmitted and incident energies, respectively. On Fig. 3, evolutions of T versus σ are shown for both arrays of period L =300 µm (Fig. 3A) and L =400 µm (Fig. 3B). We observe that T increases up to a specific value of deviation, σ M , and then decreases. There is a clear resonance of T with respect to noise. For L =300 µm and L =400 µm arrays, this relative increase of energy is respectively of 18.2 ± 0.01% and 11 ± 0.01%. The maxima of T correspond to σ M = 10.4 ± 0.5 µm and σ M = 15.4 ± 0.5 µm, only 3.4% and 3.8% of the array period, respectively. At the resonance frequency, the energy loss has been reduced by 2.7 for L =400 µm (Fig. 2). For σ ≥ σ M , T continuously decreases as one would have previously expected.

In a first attempt to describe this unexpected extra energy coupling, several models currently used to describe abnormal transmission through periodic subwavelength arrays have been tested: Block wave theory colloidal solutions properties, ionic channels activation, public opinion changes, and some complex auto organization processes 16,17,18,19,20,[START_REF] Adair | Proc. Nat. Acad. Sci[END_REF] .

A SR McNamara-like model will be used to describe our experimental data. Among the theories describing the abnormal transmission through subwavelength hole arrays, the Fano model (Figure 4A) draws an interesting parallel between the scattering process through a continuum of states interacting with an isolated state and the diffusion of light through the array 14,[START_REF] Altewischer | [END_REF]23 . The continuum of states describes the light directly crossing the array, either through the aperture, or either re emitted by the edge of the holes. And the resonant states are the surface waves. This model allows describing both propagation and scattering on complex arrays and gives good experimental data fits, and can easily be related to SR theories by the existence of discrete levels. Furthermore, it has been observed that the SR gets enhanced if an array of similar elements collectively responds to the same signal. This phenomenon has been termed the array enhanced stochastic resonance (AESR) 24,25 . We then modeled the present experiment giving the evolution of T versus σ as the sum of many individual stochastic resonance (Figure 4B), and T is the result of SPPs scattering with a global stochastic resonance, which is the sum of all SR effects between couples of levels. As a direct consequence of the choice of this model, the fitting function is given by a Lorentzian function 9

T = T o + A 1 ω 2 4 (σ -σ M ) 2 + ω 2 , (1)
where σ M is the optimum noise level and ω the width of the resonance. As can be seen in The residual part of the transmission at high noise deviations for L = 400 µm (Fig. 3B) is very similar to a sigmoid function [START_REF] Atkins | Physical chemistry[END_REF] , which describe the statistic equilibrium between two states. The total evolution of T with σ can then be described as the combination of SR theory and classical two level equilibrium theory

T = T o + A 1 ω 2 4 (σ -σ M ) 2 + ω 2 + A 2 1 + exp [(σ -σ o ) /∆σ] , (2)
Fits are shown in Fig. 3. A very good agreement between fits and experiments is observed, in both the resonance domain and the decreasing domain. The resonance width ω for L = 300 µm and L = 400 µm are found to be 21.6 µm and 9.1 µm, respectively. The resonance width characterizes the sensitivity of the SR process with the period L of hole on the screen, and highlights the sensitivity of SPPs generation and propagation to the relation between noise and periodicity. As σ increases, the arrays become closer to random hole arrays in which resonant surface waves are absent. The fraction of increased energy coupled by the resonant wave is found to be 0.14±0.01 compared to random arrays (see Fig. 3B).

In conclusion, the idea that the strong abnormal transmission only originates from the perfect periodic structure of subwavelength hole arrays should be revised. Indeed, extra energy can be coupled through the array by adding a small controlled amount of noise to the position of the holes Energy increase of about 20% has been reported, 5 fold larger than the relative noise deviation. This new transmission can be modelled with stochastic resonance theory. The evolution of the transmitted energy can be modelled as an equilibrium between a perfect organized and a completely random state, leading to the extra electromagnetic energy coupled at the surface of the screen.

From these experiments two main axes of reflection are drawn. In both visible and near infrared range subwavelength hole arrays experiments, SR effects will have important consequences. Errors on hole position of few nanometres can strongly change coupled energy and may alter experimental reproducibility and this may be a limiting factor to size decreasing in all plasmonic technologies. Furthermore, since small structural modifications have strong effects, stochastic resonance should be a powerful help in detection-related technologies. It may also lead to new interpretations and new applications in three dimensional systems dealing with phonon propagation and photonic crystals technology.

Materials and Methods

The samples are free-standing 8-µm-thick nickel-plate arrays of subwavelength squared holes, with L = 300 µm and L = 400 µm period, fabricated by electroforming. In all samples, the ratio of the surface of metal over the surface of holes is equal to 3 so that a major part of the transmitted signal is established via the SPPs. Noised arrays are generated so that the minimal distance between any parts of two nearby holes remains larger than 5 µm. All arrays have more than one thousand apertures so that the statistic of hole displacement is as close as possible to a perfect Gaussian statistic. The precision over the hole size and periodicity is better than 1 µm. For each standard deviation, a difference plate has been used, so a total of 20 plates for L = 300 µm and 30 plates for L = 400 µm. The A reference scan is taken with empty aperture. The transmission of the metal array is calculated by the amplitude ratio of the complex spectra of the metal plate and reference scan.

Fig. 3 (

 3 Fig. 3 (thin solid lines), this model reproduces very well the resonance of the transmissions for low amounts of noise. However, it does not correctly describe the evolution of the transmission for large values of σ. It could not be explained by a hypothetic inhomogeneous broadening of the resonant features by increasing noise, neither by a broadening of the

  enhanced transmission of the arrays is measured by terahertz time-domain spectroscopy (THz-TDS)[START_REF] Grischkowsky | [END_REF] . Broadband linearly polarized subpicosecond single cycle pulses of terahertz radiation are generated and coherently detected by illuminating photoconductive antennas with two synchronized femtosecond laser pulses. Numerical Fourier transform of the timedomain signals gives access to the characteristic transmission spectrum of the arrays. The transmitted electric field is recorded during 240 ps, yielding to a 3 GHz frequency precision after numerical Fourier transform, with 10 4 signal to noise ratio in 300 ms acquisition time.

FiguresFIG. 1 :FIG. 2 :FIG. 3 :

 123 Figures

Figure 3

 3

  The question of modelling this unexpected energy coupling will now be addressed. Physical systems where the increase of noise leads to a rise of the output energy can be integrated into the Stochastic Resonance (SR) framework. SR was first introduced by Benzi et al 15 in order to describe global climate oscillations between ice and temperate ages, showing that white noise could help a bistable system to change state at the same frequency than a very weak periodic coupling interaction. This model was more rigorously treated by McNamara et al9 , using master equation formalism in a system of two coupled levels in interaction with a Gaussian noise and showing that specific values of noise could increase the exchange rate of particles between the two levels. Today, SR theories have been extended to non negligible or non periodic coupling, coloured noise, non Markovian processes and finally multilevel systems, and are widely used to model neuronal signal generation, chemical reactions, some

[START_REF] Kittel | Introduction to solid state physics[END_REF]

; calculation based on pure diffraction effects, derived on Bethe diffraction theory 11 ; Composite Diffracted Evanescent Wave theory

12,13

which provides some extra adjustable parameters; Fano model

14

. Results are shown in addition to experimental data in Fig.

3B

. None of them could reproduce the observed features, since they intrinsically rely on the periodicity to explain the resonance frequencies and coupling yield.

Disorder