Nonlinear Signal Response in Electrospray Mass Spectrometry

Article pubs.acs.org/ac

Nonlinear Signal Response in Electrospray Mass Spectrometry: Implications for Quantitation of Arsenobetaine Using Stable Isotope Labeling by Liquid Chromatography and Electrospray Orbitrap Mass Spectrometry Laurent Ouerdane,†,‡ Juris Meija,† Sezgin Bakirdere,†,§,⊥ Lu Yang,† and Zoltán Mester*,† †

Institute for National Measurement Standards, National Research Council Canada, Ottawa, ON K1A 0R6, Canada Laboratoire de Chimie Analytique Bio-Inorganique et Environnement, IPREM, Université de Pau et des pays de l’Adour/CNRS UMR 5254, Hélioparc, 2 Avenue du Pr. Angot, 64000 Pau, France § Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey ⊥ Department of Science Education, Yıldız Technical University, 34220, Iṡ tanbul, Turkey ‡

S Supporting Information *

ABSTRACT: Isotope amount ratio measurements by electrospray ionization mass spectrometry show large systematic biases. Moreover, the signal ratio response can vary nonlinearly with respect to the amount ratio depending on the concentration of the analyte or coeluting matrix components, among other things. Since isotope dilution relies inherently on the linearity of response, accurate quantitation is then more difficult to achieve. In this study, we outline a method to eliminate the quantitation errors due to the effects of the nonlinear signal response. The proposed approach is a hybrid of the method of standard additions and isotope dilution allowing correction for nonlinear trend. As a proof of concept, determination of arsenobetaine content in fish tissue was performed using liquid chromatography coupled with a linear quadrupole ion trap (LTQ) Orbitrap mass spectrometer. The nonlinear isotope dilution method could, in principle, be applied to correct isotope ratio measurement biases in popular relative quantitation methods of biomolecules such as stable isotope labeling by amino acids in cell culture (SILAC), isotope-coded affinity tag (ICAT), or isobaric tags for relative and absolute quantification (iTRAQ).

Q

Although the use of isotopically enriched analytes as internal standards solves a multitude of problems associated with quantitative trace analysis, it does not eliminate the need for the calibration of the instrumental response, commonly known under the name “mass bias”. Mass spectrometry provides quantitative information in two distinct dimensions: mass and amount. Traditionally, however, these domains have also served as an ideological divide between the analyte identification and quantitation. Calibration of the mass scale is routinely performed in organic mass spectrometry, whereas calibration of the signal response is the bedrock of inorganic mass spectrometry. Observed isotope amount ratios are known to be biased, and the signal intensity response is commonly calibrated in mass spectrometry by employing the proportional error formalism (linear detector response). Mathematically, such an approach

uantitative proteomics or metabolomics form a significant part of modern analytical chemistry, yet the standards of conduct that underpin traditional measurements in analytical chemistry, are often overlooked. The majority of modern analytical methods are focused toward simultaneous screening of multiple analytes at low concentration in complex matrixes (metabolic and proteomic studies).1−4 While many studies in the past have focused on improving the identification of compounds with high resolution mass spectrometers,5−9 parallel efforts to improve precision and accuracy in the quantitation of target analytes are less numerous.10,11 At present, absolute quantitation, in the strict sense of the word according to the SI, has not matured in peptide and metabolite analysis. Peptide quantitation is now routinely performed at the relative repeatability of no better than ten percent, and certified reference materials of stable amino acids have been available only recently. Underpinning all mass spectrometry-based quantitation is the calibration of the signal response. More specifically, traceable quantitation involves the calibration of the observed (isotopic) signal intensity ratio to the corresponding amount ratio of the analytes. This is rarely done in proteomics. Published 2012 by the American Chemical Society

Received: November 25, 2011 Accepted: March 30, 2012 Published: March 30, 2012 3958

dx.doi.org/10.1021/ac203137n | Anal. Chem. 2012, 84, 3958−3964

Analytical Chemistry

Article

manifests itself by introduction of a one-variable calibration function,

R = Kr

Table 1. LC-LTQ-Orbitrap-MS Operating Conditions ESI

(1)

∼50 μA 275 °C 75 V 24 V 3.8 kV

spray current capillary temperature tube lens potential capillary potential ion spray potential

where r and R are the measured and corrected isotope ratios, respectively. In this formalism, the calibration factor K is considered a variable whose value is only affected by the variations of sample matrix and masses of measured isotopologues. The functional dependence of K on analyte ion masses gives rise to various mass-bias correction laws, such as the linear, polynomial, or exponential. Note, however, that eq 1 is not a definition, as it might be perceived. Rather, it is an assumption that the bias in the measured isotope ratio does not depend on the magnitude of the measured signal ratio itself. This assumption is often tested in thermal ionization mass spectrometry (TIMS), known as the linearity test, and no significant deviations are usually noted in TIMS or multicollector inductively coupled plasma mass spectrometry (MCICPMS) platforms. Traditional quantitation methods based on isotope dilution are developed for systems with linear concentration response. Nonlinear analyte concentration response, however, is not uncommon in analytical chemistry.12 In fact, methods such as the optical absorption and emission spectrometry13,14 or electron capture detection15 are notorious for nonlinear analytical curves. Likewise, a nonlinear concentration response is observed with the use of evaporative light-scattering detectors, which are widely used in HPLC analysis of compounds lacking a UV chromophore,16 in amperometric glucose biosensors,17 or in electrospray ionization mass spectrometry, which is widely used for peptide analysis.18,19 Quantitation based on isotope dilution, however, relies up to now on the linearity of response. Therefore, deviations from eq 1 can lead to incorrect results. Although the new generation electrospray ionization (ESI) Orbitrap mass spectrometer has permitted great advances in determination of analytes in complex mixtures such as protein digests, we demonstrate the significant nonlinear response in ESI Orbitrap MS, show its impact on the accuracy of the quantitation results, and propose a method to address this problem. The potential of the proposed method is demonstrated by the determination of arsenobetaine content in fish tissues.

MS scan mode mass resolution (m/Δm)

full scan with positive polarity 7500 HPLC

column mobile phase A mobile phase B injection volume

supelcosil LC-SCX (250 mm × 2.1 mm × 5 μm) deionized water 6 mM ammonium formate adjusted to pH = 3.0 with formic acid 25 μL

with reverse osmosis domestic feedwater (Barnstead/Thermolyne, Dubuque IA, USA). HPLC-grade acetonitrile was purchased from EMD Chemicals (Darmstadt, Germany). High-purity formic acid (w = 88%) was obtained from GFS Chemicals Inc. (Powell OH, USA). A 6 mM solution of ammonium formate (used as mobile phase) was prepared by quantitative dissolution of solid ammonium formate (Thermo Fisher Scientific, Ottawa ON, Canada) in deionized water with the pH of the obtained solution adjusted to 3.0 using formic acid. An acetonitrile/water mixture (volume ratio of 35:65) was used as mobile phase B for cleaning the HPLC column. Both 13 C-and 15N-enriched proline were purchased from Cambridge Isotope Laboratories (Andover MA, USA). Individual stock solutions of 13C- and 15N-enriched proline (1000 mg kg−1) were prepared gravimetrically in deionized water and were kept refrigerated. Both natural isotopic composition arsenobetaine and arsenobetaine with carbon-13 in its methylene moiety were synthesized in-house in the form of the nonhygroscopic hydrobromide salts.20 The chemical purity of arsenobetaine in both materials was determined by quantitative 1H NMR.20 The following purity values were obtained for the natural abundance and 13C-enriched arsenobetaine hydrobromide: 0.984 ± 0.005 g/g and 0.983 ± 0.005 g/g (expanded uncertainty, 2 SD). Individual stock solutions of arsenobetaine and 13C-enriched AsBet of 1000 mg kg−1 were gravimetrically prepared in deionized water and were kept refrigerated. A biological tissue candidate reference material (fish tissue 1; National Research Council Canada, Ottawa ON, Canada) was used as test sample for arsenobetaine. Isotopic Composition of Standards. Isotopic composition of natural amino acids or AsBet can be evaluated with high accuracy using the natural isotopic composition of the elements (IUPAC 2009) in conjunction with the binomial theorem of isotope pattern formation. For the natural AsBet, the following composition was used: [M + H]+ = C5H12AsO2, x179 = 0.940, and x180 = 0.054 (x179/x180 = 17.4). Isotopic composition of the methylene-carbon in 13C-AsBet (2-trimethyl-arsoniumyl[1-13C]acetate), x13C = 0.991(2)k=2, was obtained by quantitative 1H NMR in experiments that rely on the splitting caused by the magnetic 13C nucleus on the 1H signal of a proton directly bound to carbon. When convoluted with the remainder of the AsBet, the following isotopic composition is obtained: C5H12AsO2, [M + H]+, x*179 = 0.009

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EXPERIMENTAL SECTION Instrumentation. A Thermo Fisher high-resolution linear quadrupole ion trap (LTQ)-Orbitrap mass spectrometer (Thermo Fisher Scientific, San Jose CA, USA) was used for all measurements with ESI-LTQ-Orbitrap-MS. Optimization of the LTQ-Orbitrap was performed as recommended by the manufacturer using either a 50 ng g−1 AsBet standard solution or 200 ng g−1 proline standard solution in HPLC mobile phase. Typical operating conditions are summarized in Table 1. An Agilent HPLC 1200 Series (Agilent Technologies Canada Inc., Mississauga ON, Canada) with a cation exchange column, Supelcosil LC-SCX, and a Supelquard SCX guard column (Supelco, Bellefonte PA, USA) were used for separation of arsenic species. The coupling of HPLC to LTQ-Orbitrap-MS was accomplished by directing the eluent from the column to the LTQ-Orbitrap-MS electrospray inlet through a 50 cm polyether ether ketone tube (PEEK, 0.13 mm internal diameter). Reagents and Solutions. High-purity deionized water was obtained from a NanoPure mixed bed ion exchange system fed 3959



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Figure 1. Nonlinear signal response in Orbitrap ESI-MS. Comparison of the known (gravimetric) and measured isotope amount ratios from (a) mixtures of 13C-proline and 15N-proline and (b) the 7 mixtures of natural AsBet and 13C-AsBet prepared as detailed in the Experimental Section. Quantity R represents the isotope amount ratio as derived by gravimetry, r is the measured isotope amount ratio, and K is the ratio of the two, i.e., K = R/r.

and x*180 = 0.943 (x*179/x*180 = 0.0091). Chemical purity and synthesis of the AsBet is described in detail elsewhere.20 Isotopic composition of 13C- and 15N-enriched proline was used as specified by the manufacturer: x13C = 0.99 and x15N = 0.98. For proline, high-resolution mass spectra were acquired (m/Δm = 60 000 to 100 000) and the amount ratio of the most abundant isotopologues, [13C12C414N1H1016O2]+ (m/z = 117.074 Da) and [12C515N1H1016O2]+ (m/z = 117.067 Da), was measured. Sample Preparation for Isotope Amount Ratio Calibration. Seven mixtures of natural abundance and 13Cenriched AsBet were prepared gravimetrically. In brief, 0, 20, 40, 150, 150, 150, and 150 mg of natural AsBet standard solution (wAsBet = 15.131 mg kg−1) were accurately weighed (to within 0.1 mg) into individual precleaned 15 mL polyethylene tubes, respectively. Then, suitable amounts of 160, 160, 160, 160, 80, 20, and 0 mg of the 13C-enriched AsBet solution (wAsBet = 13.826 mg kg−1) were added to each corresponding tube. The resulting mixtures have AsBet isotopologue amount ratios in a range of 0.01 to 17.3 for ions of m/z 179 and 180. Samples were then completed to 15.0 g with 2 mM ammonium formate solution at pH = 3 prior to ESI-LTQ-Orbitrap-MS for ratio of 179/180 measurements. Mixtures of 13C- and 15Nenriched proline were prepared in an analogous manner. Sample Preparation for Quantitation of AsBet in Fish Tissues. For convenience, sample preparation was undertaken in a class-100 clean room. Nine, 250 mg aliquots of reference material (fish tissue 1) were accurately weighed (to within 0.1 mg) into individual precleaned 50 mL polyethylene tubes. Then, 0.100, 0.147, and 0.319 g of 13C-enriched AsBet standard solution (wAsBet = 13.826 mg kg−1) was added to the samples in triplicate. This was followed by addition of 25.0 g of deionized water to all samples. The tubes were capped and sonicated for 30 min. After centrifugation at 2500 rpm for 10 min, an aliquot of the supernatant (10 mL) was transferred and filtered through a 0.45 μm filter into clean 15 mL polyethylene tubes prior to HPLC-ESI-Orbitrap-MS measurements.

isotopic spike need to be known in advance. For arsenobetaine standard, we have achieved this using the quantitative 1H NMR.20 Our work with Orbitrap MS has demonstrated significant deviations from eq 1 and, on the basis of the experimental evidence, the following mass-bias formalism was employed: R = Kr b

(2)

Here, K and b are two mass-bias correction coefficients and deviations of the correction exponent (b) from the conventionally assumed value b = 1 give rise to the nonlinearity in the signal response as shown in Figure 1. The same trend could also be observed on numerous other systems, such as 2H3AsBet/AsBet, or 2H3-serine/13C-serine, which indicates the universality of the problem and of the power law trend. The reason for the nonlinearity in the instrumental response even when automated gain control is employed will require further investigation. Some potential sources of artifacts and biases with FT instruments have been presented in the literature.11,21−25 Generally, the possible sources of artifacts in isotopic distribution of mass spectra recorded with FT instruments include space charge effects between the concomitant isotopes, overfilling of the ion trap, collision of ions with background gas molecules, and FT data processing. For example, the less abundant ions are circulating on their specific trajectories in Orbitrap in lower density packets than abundant ions and therefore should be more impacted by abundant ions and background gas molecules, which may partially explain the distortion of the isotope ratios. Yet, it would be too speculative to conclude what is the origin of the nonlinear signal response. However, the aim of this work was to develop a method which is able to correct for these potential instrumental biases without the need of knowing their origin. Quantitation Using Isotopic Labeling: Proof of Concept. The quantity of the analyte in the sample can be determined with the addition of a known amount of isotopically labeled analyte. Two signals are then measured, each directly related to the analyte and spike. Using only two signals for quantitation (m/z = i and j), the method of isotope dilution takes the following mathematical description:26

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RESULTS AND DISCUSSION Nonlinear Isotope Ratio Signal Response. The applicability of eq 1 can be tested using gravimetrically prepared synthetic mixtures of analyte and its isotopically enriched analogue. For such mixtures, the known isotope amount ratio (R) is then compared with the measured isotope amount ratio (r). For this purpose, however, the isotopic composition and the chemical purity of the natural analyte and

⎛1 ⎞ ⎛ x i x*i ⎞ ⎛ a ⎞ ⎟=⎜ ⎜ ⎟·⎜ ⎟ ⎝ R j/i ⎠ ⎝ xj x*j ⎠ ⎝ a*⎠

(3)

Here, x and x* are isotopic abundances of natural and isotopically enriched analytes, respectively, and Rj/i = Rmix is 3960



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the isotope amount ratio in the spiked sample. Quantities a and a* denote the relative amount contribution of the analyte and the spike, respectively, and their ratio therefore links the amount of the added spike to the amount of the native analyte in the sample:

Although the mathematical complexity prohibits simple expressions for b, solutions for both K and b, nevertheless, can easily be obtained. To wit, the value of the amount of analyte (n) is unaffected by the changes in the amount of the added spike, and the numerical value of b that yields precisely such a situation is sought using eqs 6 or 7. In particular, the value of the exponent b is determined by minimizing the standard deviation of the obtained values of n or w (eqs 6-7) from all measured sample/spike mixtures. The numerical value of b that yields the lowest standard deviation of n or w is adopted. Such minimization can be done, for example, using the SOLVER subroutine of Excel software. This method gives identical results as minimization done during nonlinear leastsquares fitting so both of them can be employed. If uncertainties on the different measured ratios are different from each other (for example, if recorded data at the ratio 1:5 have a higher uncertainty than recorded data at ratio 1:1), then weighted nonlinear least-squares fitting should be performed. To determine the mass bias factor K, a known amount ratio of the isotopologues at m/z 179 and 180 was synthesized by mixing an appropriate amount of natural AsBet and 13C-AsBet. To achieve this, natural isotopic composition was assumed for AsBet and the isotopic composition of 13C-AsBet was obtained from 1H NMR measurements. At ratio R179/180 ≈ 1, isotope amount ratio measurement results are immune to the variation of b, which allows precise estimation of K. No difference could be observed between the expected and observed isotope ratios, i.e., K = 1. Quantitation of Arsenobetaine in Fish Tissues. The above approach of double spiking was applied to arsenobetaine determination in fish tissue candidate reference material (NRC Canada), which was recently characterized using two independent methods (standard additions and exact matching isotope dilution).20 Nine aliquots of the sample were prepared, and each three subsamples were spiked with increasing amounts of 13C-AsBet. Following the HPLC separation, mass spectrometry analysis, and data reduction, the following values were obtained: (K, b) = (1, 0.945) and nAsBet = 12.8 nmol (see Table 2). This corresponds to a mass fraction of wAsBet = 9.46

n/a = n /a (4) * * After algebraic rearrangements, eqs 3 and 4 take the following familiar form:

x R − R mix n = n · *i · * * x R −R i mix

(5)

Here, R and R* are the 179/180 isotope amount ratio in natural AsBet and 13C-AsBet standard, respectively, i.e., R = x179/x180, and R* = x*179/x*180, and Rmix is the mass-bias corrected isotope ratio of the sample spiked with the 13C-AsBet. Replacement of the true isotope amount ratio values (R) with measured values (r) in conjunction with the mass-bias model (eq 2) leads to the following: b x R − K ·rmix n = n · *180 · * b * x K ·rmix − R 180

(6)

The effect of the nonlinear signal response (b ≠ 1) can be best demonstrated with an experiment whereby several aliquots of sample are each spiked with various amounts of the spike. Even though the amount of the analyte in all samples is identical, the obtained amount will show a clear dependence on the amount of the added spike (Figure 2), clearly invalidating the method of internal isotopic standard.

Table 2. Determination of Arsenobetaine in Fish Tissue Reference Material (Average Values for Each Mixture)a Figure 2. Effect of nonlinear signal response in isotope dilution quantitation results. Six aliquots of reference material (fish tissue 1) were each spiked with a different amount of isotopically enriched arsenobetaine, and the amount of 2H3-arsenobetaine in this fish tissue was estimated using isotope dilution (eqs 2 and 5). All results are expressed relative to those obtained from the sample with rmix = 1. It is clear that the linear signal response model (b = 1) is inadequate as it produces results that vary systematically by up to 20% depending on the amount of added spike.

mixture

mass of sample,b m (g)

amount of 13CAsBet added,b n* (nmol)

measured isotope amount ratio,c r179/180 (V/V)

mass fraction of AsBet,d w (μg g−1)

1 2 3

0.2501 0.2505 0.2504

24.5 11.3 7.65

0.519 1.123 1.640

9.83 9.82 9.83

mean w ± U

9.82 ± 0.24

a

Detailed data are presented in Table S1 (Supporting Information). b Each mixture was weighted three times (average value). cAverage of six measurements (two per weigh-in). dCorrected for the 3.7% moisture content.

To determine the mass fraction of AsBet in a sample, the following equation was employed:

μg g−1 or wAsBet = 9.82 μg g−1, when corrected for the 3.7% moisture content. Uncertainty estimations were calculated following Guide to the Expression of Uncertainty in Measurement. The combined uncertainty of the grand mean, uc, was obtained by combining the uncertainties of the individual estimates (taking also into account covariance between isotopic abundances) and the variations between these means as per recent guidelines from NIST and as recently described by Yang

b M ·m x 180 R − K ·rmix * * · * b M ·m x180 K ·rmix −R (7) * −1 −1 Here, M (= 178.06 g mol ) and M* (= 179.04 g mol ), w and w*, m and m* are the molar masses of the natural and carbon-13 enriched AsBet, the mass fractions of AsBet in the sample and in the spike solution, and masses of the sample and spike solutions employed, respectively.

wAsBet = wAsBet *·

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et al.20 The value of the expanded uncertainty (U = 2 uc = 0.24 μg g−1, k = 2) is similar to what was obtained with exact matching isotope dilution, and the mass fraction of AsBet is in good agreement with the earlier independent assaying (sample being called fish1),20 which indicates that the internal calibration method is an attractive alternative to these established methods. No isotope amount ratio calibration (i.e., K = b = 1) would yield a mass fraction of AsBet in this fish tissue wAsBet = 9.46, 9.88, and 10.13 μg g−1 for mixtures 1, 2, and 3, accordingly (after the correction for moisture content). These uncalibrated values are biased from the calibrated result by up to 4% (see Table 2) and, more importantly, show significant dependence on the amount of the added spike and species concentration, which clearly indicates the shortcomings of the traditional isotope dilution method. Robustness of the Method and Other Venues of Application. Traditionally, mass bias correction is performed by analysis of an external sample which serves as a primary calibrator. In this method, however, the mass bias correction is performed in the manner of internal calibration. As a result, it eliminates the biases related to the sample matrix and to the variation in instrument sensitivity. Internal spiking is also an effective tool to demonstrate (and address) the nonlinearity in isotope ratio measurements with Orbitrap mass spectrometer. The robustness of the method was then demonstrated by screening the amount of AsBet across a wide range of isotopic ratios and using an alternative way of enrichment (triply deuterated AsBet in that case). Results obtained are presented in Figure 3 and in Table 3 for the analysis of AsBet in another

quantitation methods such as isotope-coded affinity tag (ICAT), stable isotope labeling by amino acids in cell culture (SILAC), or isobaric tags for relative and absolute quantification (iTRAQ), this approach could offer a more defendable evaluation of the isotope ratio measurement results. The information commonly obtained with these quantitation techniques is the amount ratio of the analyte with respect to its labeled counterpart as inferred from the measured isotope signal ratios. The experimentally measured isotope ratios, however, are prone to nonlinear biases as shown in this work. Such biases are more pronounced when the amount ratio of the analytes departs significantly from 1:1 and they are sensitive to coeluting species and a number of instrumental factors. As a result, analysis of a same sample which has been diluted several times can often yield to different measured isotope ratios by several tens of percent. General Remarks. In the speciation/isotope dilution context, LC ICPMS offers an extended linear range; however, it is limited in terms of specificity, because of the need for chromatographic baseline separations of complex mixtures during metabolic or proteomic studies, and it is not applicable to monoisotopic and light element (CNO) containing molecules. LC ESI MS addresses these issues; however, the dynamic range is often limited. Exact matching isotope dilution is a valuable tool, but it requires that the amount of the added labeled analyte is very close to the amount of the natural analyte. In practice, several sample preparations are performed to reach this state. In addition, when analyzing a multitude of substances simultaneously, as it is common in metabolomics or proteomics, it is practically impossible to attain exact matching for all analytes. The method outlined in this manuscript obviates such requirement. Instead, it is only necessary to analyze a few different mixtures (3 to 5) of enriched and native analytes. The arsenobetaine has been chosen here as it could be directly compared to the recently published exact matching isotope dilution method.20 Consequently, we have demonstrated that even without doing exact matching isotope dilution results of equal quality can be attained by this method in the presence of nonlinear signal response. The main advantage of this new method, however, is that it can be extended to proteomics and metabolomics studies using ESI MS involving mixing of enriched and native samples. This way, for example, the relative quantitation of numerous peptides between two different samples can be performed with improved metrological quality than is currently practiced.

Figure 3. Effect of the nonlinear signal response for quantitation of AsBet in fish tissues. Measurements of AsBet in the fish tissue were performed using 2H3-AsBet spike, and the ordinate of the plot shows the relative (normalized) calculated amount of AsBet depending on the measured isotope ratio in the sample/spike mixture (abscissa). Filled diamonds represent the values obtained from the conventional isotope dilution equations (b = 1), and open diamonds are from the proposed nonlinear isotope dilution method (b = 0.824, eq 6).

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CONCLUSIONS The often neglected contribution of Henrion’s exact matching isotope ratio calibration is a clear solution to the nonlinearity problem. This, however, requires reaching a 1:1 signal ratio between the selected ions of analyte and its labeled analogue (in these experiments, the value of K is determined from the reverse isotope dilution experiment). The nonlinear isotope dilution method proposed herein alleviates the need for reaching the exact value of 1:1 as the correct results can be obtained from any three distinct mixtures of the analyte and its labeled analogue, which resulted in similar precision and accuracy than with an exact matching isotopic dilution approach. Such an approach to nonlinear isotope ratio calibration was successfully applied in this work to determine the mass fraction of arsenobetaine in fish tissues. In conclusion, it is clear that a mere implementation of internal isotopic standards (as in isotope dilution) does not

fish tissue. The value of b is different in this new example (Figure 3 and Table 3) than during AsBet quantitation in fish tissue using C13-AsBet (Table 2) as this value is highly dependent on AsBet concentration, on sample matrix, and on instrumentation. It implies that sample dilution or preconcentration should, respectively, lead to the decrease or the increase of the value of b. Clearly, determination of b is data dependent and not sample dependent, which allows one to get corrected quantitation results regardless of the experimental conditions. The internal correction of nonlinear signal ratio response can also be employed in proteomics methods. For relative 3962



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Table 3. Detailed Data for the Example Illustrated in Figure 3 (x179 = 0.9413, x182 = 0.0002, x*179 = 0.0075, x*182 = 0.6551)a r179/182 (1/r182/179) 9.524 9.337 9.337 3.588 3.472 3.460 2.247 2.229 2.183 1.938 1.916 1.866 1.637 1.595 1.572 1.364 1.364 1.339 0.978 0.971 0.951 0.693 0.691 0.69 0.259 0.253 0.246

m, g

m*, g

w*, μg/g

n*, nmol

0.2499

0.1497

1.026

0.851

0.2490

0.3467

1.026

1.970

0.2488

0.5094

1.026

2.894

0.2497

0.5798

1.026

3.294

0.2494

0.6790

1.026

3.858

0.2493

0.7804

1.026

4.434

0.2494

1.0176

1.026

5.782

0.2501

1.3482

1.026

7.660

0.2512

3.2525

1.026

18.480

n (b = 1), nmol

relative n (b = 1)

5.642 5.531 5.531 4.906 4.747 4.731 4.506 4.469 4.377 4.419 4.368 4.253 4.365 4.253 4.192 4.176 4.176 4.097 3.888 3.861 3.780 3.632 3.621 3.619 3.185 3.113 3.022

1.454 1.425 1.425 1.264 1.223 1.219 1.161 1.151 1.128 1.138 1.125 1.096 1.125 1.096 1.080 1.076 1.076 1.056 1.002 0.995 0.974 0.936 0.933 0.932 0.821 0.802 0.779

mean w ± 2 SD a

error % 43.5

23.5

14.7

12.0

10.0

6.9

−1.0

−6.6

−20.0

n (b = 0.824), nmol

relative n (b = 0.824)

3.793 3.732 3.732 3.916 3.811 3.800 3.905 3.879 3.813 3.931 3.893 3.809 4.001 3.916 3.870 3.952 3.952 3.891 3.904 3.882 3.814 3.878 3.869 3.866 4.077 4.002 3.906

0.977 0.961 0.961 1.009 0.982 0.979 1.006 0.999 0.982 1.013 1.003 0.981 1.031 1.009 0.997 1.018 1.018 1.002 1.006 1.000 0.983 0.999 0.997 0.996 1.050 1.031 1.006

1.092 ± 0.349

error % −3.3

−1.0

−0.4

−0.1

1.2

1.3

−0.4

−0.3

2.9

1.000 ± 0.041

As a comparison, the relative uncertainty obtained with the LC ICPMS method (standard addition) was around 20%.

ensure accurate results.27 Isotope amount ratio calibration must be treated with the utmost respect when utilizing soft ionization ESI-Orbitrap-MS.

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ASSOCIATED CONTENT

S Supporting Information *

Table of detailed data for AsBet quantification in fish tissue reference material. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Margaret A. McCooeye for her technical assistance on LTQ Orbitrap MS and Paulette Maxwell for assistance with sample preparation. Scott Willie and Anthony Windust are both thanked for their characterization of the arsenobetaine standards used in this study. S.B. would like to thank Tubitak for financial support throughout this study.

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REFERENCES

(1) Breitling, R.; Pitt, A. R.; Barrett, M. P. Trends Biotechnol. 2006, 24, 543−548. 3963



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Nonlinear Signal Response in Electrospray Mass Spectrometry

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