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Journal of Lipid Research, Vol. 48, 733-744, March 2007
Control of matrix effects in the analysis of urinary F2-isoprostanes using novel multidimensional solid-phase extraction and LC-MS/MS
Department of Cardiology, Fukuoka University School of Medicine, Fukuoka, Japan Published, JLR Papers in Press, January 10, 2007.
1 To whom correspondence should be addressed. e-mail: bozhang{at}fukuoka-u.ac.jp
F2-isoprostanes (F2-iPs), established markers of oxidative stress, exist as four sets of regioisomers. Simultaneous and specific determination of F2-iPs can be achieved by liquid chromatography-tandem mass spectrometry (LC-MS/MS). We developed novel methods for urine sample preparation and HPLC to control matrix-related ion suppression effects in the LC-MS/MS analysis of F2-iPs. A selective solid-phase extraction (SPE) wash protocol was developed with an Oasis HLB (hydrophilic-lipophilic balance) SPE cartridge using an elution profile of [3H]8-iso-prostaglandin (PG)F2 (iPF2 -III) when the methanol concentration was increased under acidic, neutral, and base wash conditions. A multidimensional (MD)-SPE method that incorporated size exclusion, reverse-phase chromatography, and normal-phase chromatography was developed using an Oasis HLB SPE cartridge and an HLB µElution SPE plate. Average extraction recoveries of the deuterated internal standards of iPF2 -III and iPF2 -VI were 62 ± 8% and 60 ± 10%. A buffer-free HPLC method for the separation of F2-iP isomers was developed on base-deactivated C8 columns. Average matrix effects for iPF2 -III and iPF2 -VI were 95 ± 6% and 103 ± 5%. The clean extraction of urine F2-iPs using MD-SPE and the separation of F2-iP isomers using a novel HPLC method did not cause apparent ion suppression in the analysis of iPF2 -III and iPF2 -VI using LC-MS/MS. These findings should be useful for establishing a routine LC-MS/MS method for the analysis of F2-iPs.
Supplementary key words liquid chromatography-tandem mass spectrometry urine ion suppression effects buffer-free HPLC sample preparation iPF2
Isoprostanes (iPs) are products of the free radical-initiated autoxidation of arachidonic acid (1). F2-iPs are established markers for oxidative stress (24) and have been linked to cardiovascular diseases and risk factors (5). In addition, some F2-iPs exert potent biological activity by acting as ligands for either plasma membrane-bound prostaglandin (PG) receptors or nuclear receptors (68). F2-iPs are generated in situ esterified to phospholipids (9). Cleavage by phospholipase A2 generates free F2-iPs that are excreted in urine (10). The measurement of F2-iPs in biological samples presents several challenges. First, the methods used for measurement have to be specific, because F2-iPs are isomers of F2-PGs and exist as four sets of regioisomers (1, 11). In addition, the methods used for measurement have to be sensitive, because F2-iPs exist at very low concentrations in biological samples (1215).
F2-iPs are usually measured noninvasively in urine. The 8-iso-PGF2 Liquid chromatography-tandem mass spectrometry (LC-MS/MS) methods have been developed for the measurement of F2-iPs and their metabolites (1, 14, 15, 20). LC-MS/MS methods are specific, because HPLC can separate F2-iP stereoisomers and electrospray ionization (ESI)-MS/MS can separate F2-iP regioisomers. Also, LC-MS/MS methods are sensitive because the ESI-MS/MS technique permits the detection of very low levels of target analytes in the presence of a complex matrix background. However, LC-MS/MS is also associated with a major drawback when analyzing target analytes in biological fluids: the electrospray source is very susceptible to matrix-related ion suppression effects (21), and these matrix effects may vary from sample to sample (22).
Stable isotope-labeled analogs, which are chemically and structurally the same as the target analytes but differ in molecular mass, have been used as internal standards (IS) to compensate for variations in injection, sample preparation, instrument parameter, and matrix effects. However, interference compounds that coelute with deuterated IS of 8-iso-PGF2 Matrix-related ion suppression effects have not been examined in previously reported LC-MS/MS methods for the analysis of F2-iPs in biological samples (14, 15, 23, 24). Because the control of matrix effects is important for establishing LC-MS/MS as a routine technique for the measurement of F2-iPs in biological samples, we developed a novel urine sample clean-up technique using multidimensional (MD)-solid-phase extraction (SPE) and a novel buffer-free HPLC separation method to minimize matrix- and buffer-additive-related ion suppression effects in the analysis of F2-iPs using LC-MS/MS.
Materials All of the F2-iPs and F2-PG standards and deuterated IS of iPF2 -III, (±)5-iPF2 -VI, and PGF2 shown in Scheme 1
were obtained from Cayman Chemical (Ann Arbor, MI). Captiva Filter cartridges (0.2 µm) were obtained from Varian, Inc. (Palo Alto, CA). Oasis HLB (hydrophilic-lipophilic balance) SPE cartridges, Oasis MAX (mixed-mode anion exchange) SPE cartridges, Oasis MCX (mixed-mode cation exchange) SPE cartridges, and Oasis HLB µElution SPE plates were purchased from Waters Corp. (Milford, MA). Strata X SPE cartridges were obtained from Phenomenex (Torrance, CA). Methanol (MeOH), acetonitrile (ACN), and water were LC-MS grade (Wako Pure Chemical Industries, Ltd., Osaka, Japan). All other reagents were HPLC grade.
Tandem mass spectrometry F2-iPs were detected with a Quattro Premier tandem mass spectrometer controlled with MassLynx version 4.1 software (Waters Corp.). Ionization was achieved using electrospray in the negative ESI mode. The position of the ESI probe and parameters of MS and MS/MS tuning were optimized for maximum sensitivity by infusing 200 ng/ml 8-iso-PGF2 standard solution with a microsyringe pump (10 µl/min). The optimum tuning conditions for ESI were as follows: capillary voltage, 3 kV; source block temperature, 120°C; extractor, 3.0 V; radio frequency (RF) lens, 0.1 V; desolvation gas (nitrogen) heated to 400°C and delivered at a flow rate of 1,200 l/h; cone gas flow, 50 l/h; ion energy, 1.0; multiplier, 650 V; and low and high mass resolutions, 13. Entrance, collision, and exit for MS tuning were 50, 2, and 50 V, respectively, and entrance, exit, and collision gas (argon gas) flow for MS/MS tuning were 2 V, 2 V, and 0.35 ml/min, respectively. A fully automated instrument mass calibration (static calibration, scanning calibration, and scan speed compensation) was performed using MassLynx version 4.1 software in the ES+ mode with MS tuning parameters (capillary voltage, 3 kV; cone voltage, 40 V; source block temperature, 80°C; extractor, 3.0 V; RF lens, 0.1 V; and desolvation gas heated to 150°C and delivered at a flow rate of 350 l/h) and the NAICS calibration reference file. Waters Atmospheric Pressure Ionization Calibration solution (NaCsI; catalog No. 700001593) was introduced using the instrument's syringe pump (250 µl) at a pump flow of 10 µl/min.
Nominal mass data acquisition parameters for 2,3-dinor-8-iso-PGF2
Development of HPLC separation of isomers of F2-iPs and F2-PGs Reverse-phase HPLC was performed using Waters Alliance 2796 and 2695 Separation Modules (Waters Corp.), which were interfaced directly with the mass spectrometer. Instrument control and data acquisition were carried out with MassLynx version 4.1 software. A two pump/four solvent system was used to make the gradient. Solvent A was water, solvent B was MeOH, and solvent C was ACN. ACE 3 µm C8 50 x 2.1 mm inner diameter (i.d.) columns (Advanced Chromatography Technologies, Aberdeen, Scotland) and Hypersil BDS 3 µm C8 50 x 2.1 mm i.d. columns (Thermo Electron Corp., Waltham, MA) were used for HPLC method development and the analysis of urine samples. The HPLC separation method was developed using the computer simulation software DryLab 2000 Plus (LC Resources, Walnut Creek, CA) (25, 26). The column was held at 24°C, and the mobile phase flow rate was 0.2 ml/min. The gradient program was as follows: 06 min, linear gradient from 21% to 40.5% B/C (B:C = 2:1, curve 1); 617 min, linear gradient from 40.5% to 43.5% B/C (B:C = 2:1, curve 6); 1722 min, linear gradient from 43.5% to 100% B/C (B:C = 2:1, curve 1); and 2227 min, linear gradient from 100% to 21% B/C (B:C = 2:1, curve 1).
Development of a selective SPE procedure A selective SPE wash procedure was developed by taking advantage of the differences in the elution profiles of F2-iPs and sample matrix interference as a function of both the pH of the wash and the concentration of the elution solvents (27). The percentage of MeOH in acidic, neutral, and base washes was determined by washing the cartridges with 2% formic acid, water, and 2% NH4OH solutions containing varying concentrations (10100%) of MeOH, respectively, and collecting the waste for radioactivity counting. Elution volume was determined by eluting F2-iPs with six 0.5 ml portions of diethyl ether-acetic acid (100:2) solvent and counting the radioactivity in the eluate.
Development of a MD-SPE method
Two milliliters of centrifuged urine samples was mixed with one-fifth volume of MeOH and mixtures of IS solutions containing 8-iso-PGF2 Eluate from Oasis HLB SPE cartridges was applied to an Oasis µElution plate. SPE extraction with an Oasis µElution plate was performed using a Plate SPE Extraction Manifold (Waters Corp.). Eluate from the Oasis µElution plate was diluted with water and analyzed directly using LC-MS/MS.
Assessment of extraction recovery and matrix-related ion suppression effects
Ion suppression effects of sample matrices were examined by adding mixtures of standard solutions [2,3-dinor-8-iso-PGF2
Data analysis
MS/MS detection of F2-iPs Four groups of regioisomers of F2-iPs [groups III (15-series), IV (8-series), V (12-series), and VI (5-series)] are formed from the oxidation of arachidonic acid (11). Groups III and VI F2-iPs have been shown to be abundant F2-iPs (16, 17). Scheme 1 shows the structures of commercially available standards of group III F2-iPs [A, 8-iso-PGF2 ; G, 8-iso-PGF2ß; J, 8-iso-15(R) PGF2 ], group VI F2-iPs [L, (±)5-iPF2 -VI], F2-PG [B, PGF2 ; C, 11ß-PGF2 ; F, 5-trans-PGF2 ; H, PGF2ß; I, 5-trans-PGF2ß; K, 15(R) PGF2 ], and metabolites of 8-iso-PGF2 (M, 2,3-dinor-8-iso-PGF2 ) and PGF2 (N, 2,3-dinor-PGF2 ). Scheme 1 also shows the structures of deuterated IS of iPF2 -III (D, 8-iso-PGF2 -d4), PGF2 (E, PGF2 -d4), and iPF2 -VI [O, (±)5-iPF2 -VI-d11].
Figure 1 shows the product ion spectra of F2-iPs. Abundant molecular ions generated under the ES-mode were m/z 353 for 8-iso-PGF2
8-Iso-PGF2
Development of a reverse-phase HPLC method for the separation of F2-iP isomers
Because ammonium acetate is the common buffer additive used in the analysis of 8-iso-PGF2 The effects of pH on the separation of isomers were examined by analyzing mixtures of four standard solutions prepared with water and 0.001, 0.01, and 0.1% acetic acid, respectively. Retention of the four isomers increased with an increase in the concentration of acetic acid, but separation was not affected. Therefore, the following HPLC method was developed under neutral pH without buffer additives. The optimum temperature and gradient conditions for separation of the four isomers were determined using the computer simulation software DryLab 2000 Plus. Four experiments were performed with simultaneous changes in temperature (20°C and 40°C) and gradient steepness [gradient time, 6 and 18 min; gradient, 4090% MeOH/ACN (2:1)]. The computer simulation indicated that better separation can be achieved under a shallow gradient condition and at lower temperature.
Finally, to optimize peak shape and separation under neutral conditions, C8 columns from different makers were screened for the separation of standard solutions of six PGF2
Figure 2
shows LC-MS/MS results with the standard solutions of F2-iPs and F2-PGs. As shown in Fig. 2A, iPF2
Development of a selective SPE wash procedure Because F2-iPs are weakly acidic, weakly polar, hydrophobic compounds, three packings of polymer-based sorbents, Oasis HLB, MAX, and MCX, were screened for their ability to retain the analytes in urine samples. Figure 3A shows the breakthrough curve of [3H]8-iso-PGF2 added to a urine sample for Oasis HLB, MAX, and MCX SPE cartridges (3 cc/60 mg). As shown, [3H]8-iso-PGF2 in up to 10 ml urine sample was consistently retained by Oasis HLB cartridges but not by Oasis MAX or MCX cartridges. This result indicates that Oasis HLB had the greatest retention capacity; therefore, it was used in the following SPE method development.
To develop a selective SPE procedure, we examined the retention behavior of [3H]8-iso-PGF2 when the percentage of MeOH was increased from 0% in 10% increments at acidic pH (with 2% formic acid), neutral pH (with water), and alkaline pH (with 2% NH4OH) washes. As shown in Fig. 3B, [3H]8-iso-PGF2 was retained until the content of MeOH was increased to 50% under acidic and neutral wash conditions, but it was only retained when the content of MeOH was <20% under basic wash conditions. This result indicates that the elution profile of [3H]8-iso-PGF2 as a function of MeOH concentration was different at low and high pH. According to these results, a selective SPE procedure was developed and incorporated into MD-SPE.
MD-SPE of urine samples for LC-MS/MS analysis Eluted fraction A from the HLB SPE cartridge was applied to the HLB µElution plate after dilution with hexane (Fig. 3C). In this step, F2-iPs were retained on the SPE sorbent by normal-phase chromatography. In plate wash step 1, acetic acid was washed off with 5% MeOH (Fig. 3C). In plate wash step 2 (base wash), yellow interference was washed off with 5% MeOH and 2% NH4OH. In plate wash steps 3 and 4, the pH was switched to acidic by washing with 5% MeOH and 2% formic acid, and formic acid was subsequently washed off with 5% MeOH (Fig. 3C). In plate wash step 5, moderately polar, hydrophobic interference was washed off with 15% MeOH. Finally, in elution fraction step B, F2-iP fractions were eluted with 80% MeOH. The final eluted fraction was clear and used directly for LC-MS/MS analysis after dilution with water.
Analysis of urine extracts using LC-MS/MS
To examine whether or not iPF2 -III and iPF2 -VI were quantitatively recovered from different volumes of urine samples, 1 and 2 ml urine samples from eight volunteer subjects were spiked with the same amount of iPF2 -III-d4 and iPF2 -VI-d11 (2 ng) and extracted using the MD-SPE method. Figure 5
shows that the relative areas of iPF2 -III to iPF2 -III-d4 (Fig. 5A) and iPF2 -VI to iPF2 -VI-d11 (Fig. 5B) in 2 ml urine samples were well correlated (r = 0.992 and 0.997, respectively) with those in 1 ml urine samples. The signal-to-noise ratios for iPF2 -III (Fig. 5C) and iPF2 -VI (Fig. 5D) ranged from 16 to 118 and from 143 to 355, respectively. As shown in Fig. 5, the signal-to-noise ratios for iPF2 -III (Fig. 5C) and iPF2 -VI (Fig. 5D) extracted from 2 ml urine samples were greater than those extracted from 1 ml urine samples. These results indicate that peak-to-peak signal-to-noise ratios of >20 were achieved for iPF2 -III and iPF2 -VI analysis by extracting 2 ml urine samples from eight randomly selected volunteers.
SPE recovery and matrix-related ion suppression effects IS mixtures of 8-iso-PGF2 -d4 and (±)5-iPF2 -VI-d11 (2 ng) were added to 1 or 2 ml urine samples before and after extraction to examine sample extraction recovery (Table 1
). As shown in Table 1 (extraction 1), 5070% of the IS was recovered from 1 and 2 ml urine samples from four volunteer subjects. Four repetitive extractions (extractions 14) of 2 ml urine samples from four subjects showed consistent recoveries, and the average recoveries for iPF2 -III-d4, iPF2 -VI-d11, and 5-epi-iPF2 -VI-d11 were 62 ± 8%, 60 ± 10%, and 61 ± 8%, respectively (Table 1).
The effects of urine matrix on the ionization efficiency of F2-iPs were examined by comparing the ion intensities of standard solutions in water and urine sample matrices. As shown in Table 2 , 1223% of the ion suppression (matrix effects, 7788%) was consistently observed for 2,3-dinor-iPF2 -III, which was extracted from 1 and 2 ml urine samples (extraction 1) or at different times (extractions 14). The matrix effects for 1 and 2 ml urine samples and different extractions on other F2-iPs ranged from 88% to 127% (Table 2), and the average matrix effects for 15(R) iPF2 -III, iPF2 -III, iPF2 -III-d4, iPF2 -VI, 5-epi-iPF2 -VI, iPF2 -VI-d11, and 5-epi-iPF2 -VI-d11 were 95 ± 6%, 100 ± 6%, 103 ± 5%, 96 ± 3%, 100 ± 3%, 109 ± 15%, and 104 ± 16%, respectively. These results indicate that the ion suppression effects of urine matrices did not significantly affect the ionization efficiency of these F2-iPs.
Oxidative stress is related to many diseases, including cardiovascular disease (2, 3, 16, 17). Methods for the routine measurement of markers of oxidative stress are urgently needed. F2-iPs are products of the reactive oxygen species-mediated peroxidation of arachidonic acid and have been shown to be reliable markers of oxidative stress (1, 4, 5). LC-MS/MS methods have recently been developed for the specific determination of F2-iP regioisomers in biological samples (14, 15, 23, 24). However, matrix effects are not controlled in these methods, which are known to affect the accuracy, reproducibility, and sensitivity of ESI-MS (21, 28, 29). In this work, we developed a novel MD-SPE and buffer-free HPLC method to control matrix- and buffer-additive-related ion suppression in the LC-MS/MS analysis of F2-iPs in urine samples. We developed the MD-SPE method based on two-step SPE, applying orthogonal retention mechanisms, and on a selective SPE wash and elution protocol for F2-iPs. In the first-step SPE on Oasis HLB SPE cartridges, F2-iPs were retained by a reverse-phase chromatography mechanism, and in the second-step SPE on an Oasis µElution SPE plate, F2-iPs were retained by a normal-phase chromatography mechanism. Because Oasis HLB is a hydrophilic-lipophilic balanced polymer sorbent (27), both reverse-phase chromatography and normal-phase chromatography mechanisms can be used for the retention of F2-iPs. The solvents were exchanged for LC-MS/MS analysis in the second-step SPE, which eliminated the need to evaporate organic solvents that is normally part of the SPE of urine samples (14, 15, 23, 24). Also, the samples were concentrated using small-bed SPE sorbent (2 mg) in the second-step SPE (Fig. 3C). Concentration is normally achieved by the evaporation of organic solvent, and both target analytes and matrix interference are concentrated. However, in the second-step SPE on the Oasis µElution plate, F2-iPs were concentrated but matrix interference was removed, which further cleaned up the samples. Because of the small elution volume (40 µl), a 10-fold concentration of 2 ml urine samples was easily achieved by the MD-SPE method. In addition, using MD-SPE, the time required to prepare samples was greatly shortened, because organic solvents did not have to be evaporated. In MD-SPE, the clean extraction of urine samples was achieved by a novel selective SPE wash and elution procedure. Oasis HLB is a polymer sorbent and can be used from pH 1 to 14 (27). Therefore, a selective SPE wash procedure was developed by taking advantage of the different elution profiles of F2-iPs and urine matrix interference as a function of both the concentration of MeOH and pH. With HLB sorbent, acid and base compounds show opposite retention behaviors under low and high pH. Under low pH, acid compounds have strong retention and base compounds have weak retention, whereas under high pH, acid compounds have weak retention and base compounds have strong retention. Therefore, when acidified urine samples containing 10% MeOH were applied to an HLB SPE cartridge, base interference was not retained. Acidic wash with 15% MeOH/2% formic acid (Fig. 3C, cartridge wash step 4) was also used to eliminate base interference. Base wash with 5% MeOH/2% NH4OH was used to remove acid interference. Elution of yellow interference was observed during the base wash. Neutral interference in the urine samples was washed off with hexane. Because hexane is immiscible with MeOH and water, one part of diethyl ether was added to the wash solvent (Fig. 3C, cartridge wash step 5). A wash step with hexane-ethyl acetate (9:1) (Fig. 3C, cartridge wash step 6) was further included to remove residual water on the HLB SPE cartridge because ethyl acetate is miscible with water. Diethyl ether/2% acetic acid was used for the elution of F2-iPs in the first-step SPE because diethyl ether is less polar and more selective than ethyl acetate. Therefore, selective wash and selective elution gave a selective SPE procedure for the clean extraction of F2-iPs. The cleanliness of the extracted urine samples as examined by MS was not markedly affected by slight variations in extraction parameters, including the concentration of organic solvent and pH (data not shown), indicating that the selective SPE procedure was robust. Also, the use of Strata X SPE cartridges, another polymer sorbent, instead of Oasis HLB SPE cartridges did not affect the cleanliness of extraction or recovery (data not shown), indicating that the MD-SPE method is robust.
Because F2-iPs are isomers of F2-PGs and consist of many diastereomers (1, 11), separation of these isomers is important for the specific analysis of individual F2-iPs. Li et al. (15) showed that 15(R) 8-iso-PGF2 Because we found that buffer additives caused significant ion suppression of F2-iPs and the separation of F2-iP isomers was not affected by including acetic acid in the extracted urine samples (data not shown), an HPLC method was developed without the use of buffers to control pH. Alternatively, we used LC-MS-grade water for LC-MS/MS analysis. Buffer-free HPLC methods minimize the maintenance of the LC-MS/MS machine and save time required for the daily preparation of buffers. Only water, MeOH, and ACN were supplemented. The novel HPLC method is robust because slight variations in temperature, mobile phase composition, gradient steepness, pH, sample volume, and replacement of HPLC columns did not significantly affect the separation of the commercially available F2-iPs standards (Scheme 1) (data not shown). To demonstrate the robustness of the novel HPLC method, we also analyzed standard solutions and extracted urine samples in different HPLC machines with different system volumes (Waters Alliance 2796 and 2695 Separation Modules). Similar separation of F2-iPs was achieved by changing the prevolume parameter (300 and 600 µl for Waters Alliance 2796 and 2695 Separation Modules, respectively) and slightly adjusting the starting gradient organic content while keeping the gradient steepness constant (data not shown). This is the first report that a robust HPLC method for the separation of F2-iPs was efficiently developed using computer simulation software. This agrees with the finding of Snyder and Dolan (26) that the separation of stereoisomers as a function of temperature and gradient was predictable by a computer simulation using DryLab.
We found that the maintenance of HPLC columns and MS detectors could be minimized using the novel MD-SPE and HPLC methods. More than 400 injections of the extracted urine samples did not cause a significant increase in HPLC column backpressure (data not shown). Therefore, guard columns and precolumn filters were not used in the HPLC analysis. More than 40 injections of the extracted urine samples did not cause visible contamination of the sample cone in the MS detector. This not only saves time for MS maintenance but also reduces the variation in detection sensitivity. Also, our findings indicate that these novel MD-SPE and HPLC methods made possible the consistent recovery of IS of iPF2 One great advantage of the novel MD-SPE method is that the urine sample-processing time for LC-MS/MS analysis is short. We normally extract eight urine samples in 3 h. Because of the robustness of the MD-SPE method, it should not be difficult to increase sample throughput through automation. Also, the MD-SPE method can be used to process 10 ml of culture medium from cells, including endothelial cells and smooth muscle cells, or 1 or 2 ml urine samples from animals, including rabbits and rats, with only very slight modification [i.e., by replacing a 0.2 µm, 3 ml Captiva Filter cartridge with a 10 µm, 10 ml Captiva Filter cartridge (Varian, Inc.)] (data not shown).
However, the MD-SPE method will require major modifications if plasma samples are to be prepared for the analysis of F2-iPs using LC-MS/MS. Because F2-iPs are generated in situ esterified to phospholipids (1), alkaline hydrolysis of plasma samples is needed to cleave F2-iPs into free F2-iPs to measure total F2-iPs. Also, it may be worthwhile to add a free radical scavenger such as butylhydroxytoluene or an inhibitor of cyclooxygenase such as indomethacin (30) to EDTA plasma samples to prevent autoxidation during sample separation, storage, and processing. Iuliano et al. (31) added [2H8]arachidonic acid to plasma samples after collection to detect any artifactual formation of 8-iso-PGF2
In conclusion, we developed a novel sample clean-up method using MD-SPE and a novel HPLC method for the specific analysis of F2-iPs using LC-MS/MS. With this novel MD-SPE LC-MS/MS method, it should no longer be difficult to perform the routine analysis of F2-iPs in urine samples. Validation of the novel MD-SPE LC-MS/MS method for the routine analysis of iPF2
The authors thank Ms. Yuri Saito and Ms. Rieko Teruya for assistance in processing samples. This work was supported by a grant-in-aid from the Ministry of Education, Science, and Culture of Japan (No. 18591009).
Submitted on
October 2, 2006
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