Quantitative Mass Spectrometry Independence from Matrix Effects and

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Quantitative Mass Spectrometry Independence from Matrix Effects and Detector Saturation Achieved by Flow Injection Analysis with Real-Time Infinite Dilution Sergio C. Nanita* DuPont Crop Protection, Stine-Haskell Research Center, 1090 Elkton Road, Newark, Delaware 19714, United States S Supporting Information *

ABSTRACT: A high-throughput quantitative analysis method is presented to determine analyte concentrations at the infinite dilution limit, where the presence and effects of matrix become null, achieving mathematical independence from the detrimental phenomenon of matrix effects. Dilution is achieved online, reproducibly and in seconds by diffusion/mixing that occurs in flow injection analysis, while analyte concentration measurements are made by electrospray ionization tandem mass spectrometry. Because of matrix effects, the measured analyte concentration (Am) was inaccurate at high matrix concentrations, but accuracy consistently improved as matrix concentration was reduced by dilution. The method provides a practical solution around the decades-long matrix effects problem in quantitative analytical chemistry without separation of analytes from the matrix (e.g., chromatography) or use of corrective procedures, such as matrix-matched standards or isotopically labeled internal standards. Broad applications were demonstrated for part-per-billion quantitation of bioactive molecules (pesticides) in extracts of food, plant tissues, and body fluids by coupling the method to a high-throughput sample extraction/cleanup based on salting out with ammonium formate. The technique provides an assessment of matrix effects with remarkable comprehensiveness, simplicity, and speed. A limit of quantitation of 10 ng/g, a level appropriate for pesticide residue analysis and bioanalytical applications, was demonstrated. The method is also independent of detector saturation; this feature increased the applicable concentration range 20−100-fold above that of conventional techniques. In the abstract graphic, the measured analyte concentration (Am) approaches the accurate value (A0) when matrix effects disappear as measurements are conducted while lowering the normalized sample concentration (Snorm) by real-time dilution.

T

allowed accurate quantitative analysis of metals in complex matrixes by atomic emission/absorption spectrometry.6 A similar extrapolative dilution method was later proposed by Kruve et al. for LC/MS analysis.7 A limitation of these extrapolative dilution methods is that dilution is performed manually as part of sample preparation.6,7 Consequently, throughput is relatively low and the data points obtained are limited to the number of dilutions prepared.6,7 Liquid chromatography, which is used for online separation of sample components prior to mass spectrometry detection,7 also limits analytical throughput. Today, dilution is the main sample preparation step performed for matrix reduction in popular “dilute-and-shoot” LC/MS methods.8,9 On the other hand, flow injection analysis, a technique known to facilitate high-throughput online sample dilution,10,11 has remained underutilized in trace-level analysis of small organic molecules by mass spectrometry. Flow

race-level chemical measurements in complex matrixes are essential for daily operations of society including clinical diagnostics, manufacturing, food safety, law enforcement, commodity trade, and development of bioactive molecules such as pharmaceuticals and agrochemicals. Several analytical techniques applied for these purposes suffer from a limitation that has hindered their performance for decades: matrix effects.1 For example, in mass spectrometry (MS), matrix effects are intrinsic to ionization processes2 and detrimental to the accuracy of quantitative measurements.3 Current MS methods address this limitation mainly by separating the analytes from matrix which is typically done by liquid chromatography (LC) and/or correcting for matrix effects via calibration methods such as matrix-matching and isotopically labeled internal standards.4 It is known that dilution of samples can improve quantitative measurements by lowering the amount of matrix that is present during analysis. For example, reduction of interferences in flame spectrophotometry was reported by Beckman and co-workers in 1950.5 Thompson and Ramsey introduced the extrapolative dilution approach in 1990, which eliminated matrix effects and © XXXX American Chemical Society

Received: August 12, 2013 Accepted: November 14, 2013

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Figure 1. Illustration of the dilution profile achieved in flow injection analysis during transport of the sample band, where S = sample concentration. The method provides a suitable option for real-time (online) sample dilution with duplicate sets of a concentration range obtained at the first and second half of the peak (front and tail). It can be assumed that the maximum sample concentration (Smax) at the peak apex (tmax) represents the time when the maximum analyte concentration (Amax) and maximum matrix concentration (Mmax) occur, since the injected sample is diluted in-transit without separation of its components.

Supporting Information). Additional spike levels were prepared for hexazinone in blood extracts from 0.01 ng/mL to 100 ng/ mL to evaluate the method applicable analyte concentration range. The main purpose of these experiments was to characterize the performance of the measurement method (real-time infinite dilution by FIA/MS/MS), not the sample extraction, because the extraction method has already been rigorously tested.22 Another experiment was designed to test the overall method performance with field samples and control samples spiked directly onto the specimens prior to extraction, as detailed below. Quantitation of Chlorantraniliprole in Strawberry Experimental Field Samples. Two separate 3.0-g aliquots of each strawberry sample taken from an experimental field were weighed into 50-mL propylene centrifuge tubes. The same extraction procedure described above for other food samples was followed. Then, each acetonitrile-rich (top) layer was diluted by mixing a 100 μL aliquot with 900 μL of acetonitrile. The resulting samples were analyzed by the concept method. The volumes of acetonitrile-rich layers (post salting out) were measured to be 9 mL; this value was used in the calculation of chlorantraniliprole residues in strawberry samples. The same sample preparation and extraction procedure was followed for aliquots of a control sample that were spiked with chlorantraniliprole at 0.010 mg/kg, 0.20 mg/kg, and 4.00 mg/kg. Sample fortification was performed directly onto the 3.0-g strawberry aliquots prior to extraction. Flow Injection Tandem Mass Spectrometry Conditions. The instrumental conditions used were adapted from recently reported FIA/MS/MS methods.17,22 Applied Biosystems/Sciex (Foster City, California) API-5000 triple quadrupole mass spectrometers were used. Two separate units of the same model were employed to test different features of the technique and confirm method reproducibility. These instruments were equipped with electrospray ionization sources. Agilent 1290 HPLC instruments (Agilent Technologies, Wilmington, Delaware) were coupled to the mass spectrometers by connecting the autosampler directly to the electrospray source with a 150 cm PEEK capillary of 0.13 mm inner diameter (part number 0890-1915, Agilent Technologies, Wilmington, Delaware). This allowed the systems to be operated in FIA/MS/MS mode. The carrier solvent matched the diluted reagent blank composition (see the Supporting Information) and was pumped at a flow rate of 100 μL/min. The sample injection volume was 10 μL. Note that these FIA parameters were optimized to allow fast analysis while still achieving acceptable sensitivity, precision, and accuracy for the

injection analysis (FIA) delivers real-time sample dilution with every injection via diffusion and mixing that occurs as the sample band travels from the injector to the ion source, as illustrated in Figure 1. Uses of this phenomenon are common12−14 and allow rapid physicochemical measurements, such as determination of binding and dissociation constants.10,14 In addition, FIA/MS/MS has been progressively improved15−17 with well-established calibration methods4 for trace-level analysis in complex matrixes across disciplines with adequate selectivity.16 For example, FIA/MS/MS methods have been reported and applied to pesticide residue analysis,15−17 authenticity assessment,18 bioanalysis,19 and multivitamin analysis.20,21 Herein, a method that merges principles from the techniques described above is introduced for fast analyte concentration measurements at the infinite dilution limit, where matrix concentration is infinitesimal and matrix effects are null. The method uses the real-time dilution achieved in FIA (Figure 1) for high-throughput determinations by tandem mass spectrometry across a range of sample concentrations. The main assessment of the technique has been conducted with electrospray ionization, since it is among the most widely used methods. Mathematical and experimental demonstrations of this method are presented.

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EXPERIMENTAL SECTION Extraction of Biological Fluids and Food Samples. The sample extraction procedure was adapted from a recently reported high-throughput ammonium salting out method which was designed to be compatible with FIA/MS/MS.22 Control samples (1.0 g) of rat urine and blood, strawberry, corn meal, wheat grain, and canola seed were weighed into 50-mL propylene centrifuge tubes. A volume of 10 mL of acetonitrile was added to each tube, and the samples were swirled. This was followed by addition of 10 mL of the salting out agent, aqueous ammonium formate 34% w/w. The tubes were capped and vigorously shaken for 1 min. After centrifugation, the acetonitrile-rich (top) layer was diluted 10-fold with acetonitrile, i.e., 1.0 mL aliquot mixed with 9.0 mL of acetonitrile diluent. The resulting extracts were spiked with the analytes of interest from high-level stock solutions. Extracts of rat urine, wheat grain, strawberry, canola seed, and corn meal were spiked at 1.0 ng/mL and 5.0 ng/mL with hexazinone, flupyrsulfuron methyl, and triflusulfuron methyl. Extracts of whole rat blood were spiked with hexazinone, flupyrsulfuron methyl, triflusulfuron methyl, and chlorantraniliprole at 100 ng/mL and 500 ng/mL (chemical structures appear in Table S-1 in the B

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intended applications. Conditions could be varied to obtain different method performance suited for other purposes. The electrospray ion source conditions used were curtain gas (CUR) 28 arbitrary units, GS1 30 arbitrary units, GS2 30 arbitrary units, spray voltage 4200 V, temperature 500 °C. MS/ MS ion transitions were recorded for the compounds of interest. These fragmentation reactions were demonstrated to produce adequate selectivity, as confirmed by analysis of control samples of every matrix tested. The dwell time for each ion transition was 5 ms, which allowed collection of sufficient data points over the 30-s MS/MS data acquisition time. Total flow injection analysis run time was set to 60 s, which allowed the system to be flushed thoroughly between injections. Additional MS/MS conditions appear in Table S-2 in the Supporting Information. System Calibration. FIA/MS/MS data were recorded from a single reference standard solution prepared in reagent blank at 1.0 ng/mL or 5.0 ng/mL (depending on analyte response), injected in triplicate. Note that the noise filter options (i.e., smoothing and bunching factor) provided by the Analyst 1.5 instrument data acquisition software (Applied Biosystems/Sciex) were not used. Instead, the resulting MS/ MS ion chronogram raw data points (signal intensity vs time) were copied into a Microsoft Excel worksheet and averaged. This process resulted in MS/MS averaged ion chronograms that were then binned, such as the example shown for hexazinone in Figure 2a,b. A bin size of 20 points was used with 50% overlap between bins; that is, distance between bin centers = 10 data points. Averaging triplicate injections and data binning across the time axis reduced noise and improved measurement precision and accuracy. The next step in the system calibration process involved calculation of analyte response factors, RA(t) = I(t)/A, across time. These RA(t) values are specific to their corresponding time in the flow injection analysis experiment. Note that this was only done for data points with a signal-to-noise ratio (S/N) > 3. A representative example is shown in Figure 2c. These RA(t) values are used later in the analysis of samples to calculate Am (measured analyte concentration). Conversion of Abscissa from “Time” to “Snorm”. The averaged/binned standard data sets (e.g., Figure 2b) were used to calculate the normalized sample concentration, Snorm, at each time point. This was done by dividing the signal intensity at each time point by the maximum signal intensity that occurred at the peak apex. This newly created data column now allowed the time dimension (x-axis) to be converted to normalized sample concentration, Snorm. As shown in Figure 3, this exercise elucidated the dilution profile of the FIA system as a function of time. Note that the resulting Snorm(t) is applicable to the concentration of every component (matrix and analyte) in a standard or sample, because it is assumed that the components are not separated in flow injection analysis. Also, using both sides of the peak for system calibration, and later for sample analysis, essentially provided a duplicate experiment across the sample dilution range (see the abstract graphic and Figure 3b). Plotting Am vs Snorm from Raw Data. The sample extracts were injected for analysis using the exact same conditions and acquisition method employed for system calibration. Samples were injected in triplicate. The resulting data were averaged and binned as described for reference standards, unless otherwise indicated. The Am data points were calculated based on the RA(t) previously obtained from reference standards (e.g., Figure 2c) and signal intensities from the averaged/binned sample

Figure 2. (a) Average MS/MS ion chronogram (m/z 253 → m/z 171) obtained for a 1.0 ng/mL hexazinone standard prepared in reagent blank. (b) Resulting chronogram after the binning process. (c) Analyte response factors, RA(t), obtained for hexazinone as a function of time.

chronograms; that is, Am = I(t)/RA(t). Then, the results were used to graph Am vs Snorm, as shown in the abstract graphic. Some sample chronograms needed to be synchronized with the reference standards chronograms. This was done by shifting the sample data points along the time axis, as shown in Figures S-1 and S-2 in the Supporting Information, such that the intensity maxima of both data sets were aligned. This important step is discussed further in the Supporting Information. Regression Analysis to Obtain the Am(Snorm) Function and A0. Regression analysis was conducted using Minitab 16.2.2, particularly the nonlinear regression tool of the software. Note that this software is not a requirement for data analysis but rather a tool employed in this study; other statistical or mathematical software could be used. The analysis for all C

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analyte, I, divided by the concentration, A. This relationship can be written as I = RA ·A

(1)

However, in the presence of matrix (for example, infusion of a sample extract), signal intensity can be affected by matrix effects, thus I = RAM·A

(2)

where RAM is the analyte response factor in matrix. Then, matrix effects, ME, can be defined as

ME =

RAM RA

(3)

and, merging eqs 2 and 3 results in the following expression: I = ME·RA ·A

or

A=

I ME·RA

(4)

Note that ME is defined in eqs 3 and 4 for a specific matrix concentration. However, it is known that matrix effects vary as a function of sample dilution.7,9 Therefore, ME must be a function of the matrix concentration, M. Types of matrix effects and possible situations can be categorized as follows: ME < 1 when matrix suppression occurs, ME > 1 in cases of matrix enhancement, and ME = 1 when matrix effects are absent or matrix is simply not present. The latter case can theoretically occur if a sample is infinitely diluted, and this state results in annulment of ME:

Figure 3. (a) Normalized sample concentration, Snorm(t), versus time calculated from the binned data displayed in Figure 2b for a 1.0 ng/mL hexazinone standard prepared in reagent blank. (b) Plotting time vs Snorm, as displayed in panel b, highlights that duplicate sample dilution is obtained in each data set and also shows the spread of FIA/MS/MS ion chronogram data points (peak front, tail, and apex) across the Snorm abscissa. Note that measured analyte concentrations (Am) should be graphed as a function of this newly created Snorm(t) when using the real-time infinite dilution approach to obtain A0, as described in the Results and Discussion.

lim ME = 1

(5)

S→0+

where S is the sample concentration ranging from Smax to zero in a dilution series; that is, from the maximum sample concentration to the sample concentration at infinite dilution conditions. Under infinite dilution conditions, eq 4 simplifies to A = (I/RA). It shows that A, if calculated with experimental RA and I measurements as a function of S, becomes independent of ME at the infinite dilution limit. Although it is physically impossible to perform measurements with infinitely diluted samples, the initial hypothesis was that experimental measurements of this limit may be achievable and practical with flow injection analysis. That is, analyte concentration measurements could be performed with real-time dilution by FIA/MS/MS; the measured analyte concentration, Am, may be inaccurate at relatively high sample concentration due to high levels of matrix, but accuracy must improve as S decreases, profiling the Am vs S function which could be elucidated by regression analysis. Finally, Am at infinite dilution conditions, A0, could be obtained as indicated below:

samples started by nonlinear regression based on the first order exponential equation Am(Snorm) = a · eb(Snorm) using the following settings: starting value for a = 0, starting value for b = 0, confidence level for all intervals = 95%, algorithm = Gauss− Newton, maximum number of iterations = 1000, convergence tolerance = 0.0001. The limit of the Am(Snorm) function when Snorm approached zero from positive values, i.e., A0, was requested as an additional output in each regression analysis with its corresponding two-sided 95% confidence interval. Plots of Am vs Snorm as well as residual graphs were also created as outputs of the analysis. A second order regression analysis based on the function Am(Snorm) = a · eb(Snorm) + c · ed(Snorm) was then conducted for all samples. The same parameters listed above were used, except that starting values for a and b were set to the results reported on the first order exponential regression analysis, while starting values for c and d were both set to zero. The additional outputs were also obtained: A0 with its twosided 95% confidence interval and plots of Am vs Snorm and residuals.

lim A m (S) = A 0

S→0+

(6)

This hypothesis suggests that A0 could be determined without physically separating the analyte from the matrix and without corrective procedures, such as isotopically labeled internal standards. Mathematical Considerations for Quantitative Analysis by FIA with Real-Time Infinite Dilution. As shown in Figure 1, dilution occurs over the time axis in FIA, resulting in a time-dependent sample concentration function, S(t). Consequently, signal intensity, which is a function of sample concentration, will also vary with time. Note also that the exact concentration of the sample at each time point in FIA

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RESULTS AND DISCUSSION Independence from Matrix Effects at Infinite Dilution Conditions. Let us consider an electrospray mass spectrometry experiment where a solution containing an analyte of interest is continuously infused at a constant flow rate into the ion source until a stable signal intensity is obtained. In this example, the analyte response factor in the clean standard solution, RA, can be defined as the signal intensity of the D

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chronograms does not need to be known. Instead, S(t) can be normalized as follows: Snorm(t ) =

S(t ) I (t ) = Smax Imax

Table 2. Description and Abbreviations of Parameters Independent of Time in Quantitative Analysis by Flow Injection Analysis (FIA) with Real-Time Infinite Dilution parameter

(7)

A

where Snorm(t) is the normalized sample concentration function that describes the real-time dilution observed in a particular FIA method, Smax is the maximum sample concentration which occurs at the FIA peak apex with signal intensity Imax. Because chemical separation should not occur in FIA, it can be assumed that the normalized sample concentration function Snorm(t) represents the dilution profile of both analyte and matrix over time. Similarly, the analyte response factor (RA) can be redefined as a time-dependent function, which can be calculated using the injected analyte concentration in a calibration standard, as shown in Figure 2c. This approach allows profiling the analyte response factor function in each FIA calibration experiment; therefore, eq 1 becomes RA(t ) =

I (t ) A

Amax A0 Mmax Smax a

The maximum concentrations (Amax, Mmax, Smax) occur at the peak apex in FIA chronograms. Although these parameters are not dependent on time, they are dependent on the exact experimental conditions, such as carrier solvent used, flow rate, and sample injection volume, which may affect their magnitude as well as the peak apex position in FIA chronograms. bIn theory, if A0 is a perfectly accurate measurement of the analyte concentration in the injected solution, it can be considered that A0 = A for mathematical purposes (e.g., derivation of eq 15).

canola seed were extracted and fortified with pesticides at 1.00 ng/mL and 5.00 ng/mL. Concentrations of the analytes in these fortified extracts were then quantified using the proposed method. The experimental data obtained for Am(Snorm) vs Snorm was observed to follow first and second order exponential functions:23

(8)

where I(t) is the time-dependent signal intensity and A is the analyte concentration in the injected solution. Note that all parameters that are dependent on S, I, and/or RA now become dependent on time. This is the case of measured analyte concentration, which is defined below as a function of timedependent I(t) and time-dependent RA(t): I (t ) A m (t ) = RA(t )

(9)

lim

A m (Snorm) = A 0

(10)

For clarity, descriptions of mathematical functions dependent on time and parameters independent of time appear in Tables 1 and 2, respectively. Table 1. Description and Abbreviations of Time-Dependent Functions Relevant to Quantitative Analysis by Flow Injection Analysis (FIA) with Real-Time Infinite Dilution time-dependent function in FIA experiments S(t) I(t) RA(t) RAM(t) ME(t) Am(t) Snorm(t)

A m (Snorm) = a ·eb(Snorm)

(11)

A m (Snorm) = a ·eb(Snorm) + c·ed(Snorm)

(12)

where a, b, c, and d were parameters obtained by nonlinear regression. On the basis of eq 10, A0 = a in the first order exponential regression model (eq 11); while A0 = a + c in the second order exponential regression model (eq 12). Matrix effects of diverse magnitudes were observed across the specimens tested, a known challenge in trace-level quantitative analysis.7,24 Figure 4 shows data obtained for hexazinone spiked at 1.0 and 5.0 ng/mL in corn meal, rat urine, and canola seed extracts as example cases with minor, moderate, and severe matrix effects, respectively. Note that a worst-case scenario was exemplified by canola seed, which is known to cause severe matrix suppression22 likely due to the presence of high oil levels; nevertheless, accurate measurements were possible for hexazinone. Several interesting features are present in data displayed in Figure 4 and Figure S-3 in the Supporting Information. For example, signal distortions are noticeable under severe matrix suppression, resulting in a split peak for hexazinone in canola seed extract. This occurs when matrix suppression weakens upon dilution at a greater rate than signal reduction due to decreasing analyte concentration. In principle, the resulting signal should split symmetrically; however, the asymmetry is likely due to residual of matrix components (e.g., oils) in/on the ion source which could result in prolonged matrix effects. Consequently, only peak-front data points were used (without binning) for analyte quantitation in canola seed extracts to ensure measurement accuracy. Surface/matrix interactions during transport of the FIA sample band from the injector to the ion source could also be responsible for the observed asymmetric signal distortion (Figure S-3 in the Supporting Information). However, if that is the case, matrix/analyte separation should occur. The accurate result obtained for

where Am(t) is the measured analyte concentration as a function of time across the FIA chronogram. Note that, once FIA data are recorded, Am(t) can be graphed as a function of Snorm(t); thus, eq 6 becomes Snorm → 0 +

description analyte concentration in the injected solution (also referred to as “analyte added”) maximum analyte concentrationa measured analyte concentration (Am) at infinite dilution conditionsb maximum matrix concentrationa maximum sample concentrationa

description sample concentration signal intensity analyte response factor in reagent blank analyte response factor in matrix matrix effects measured analyte concentration normalized sample concentration

Experimental Validation of Quantitative Analysis by FIA/MS/MS with Real-Time Infinite Dilution. Control samples that represented applications of quantitative mass spectrometry in agricultural chemistry, food safety, toxicology, and bioanalysis were selected to demonstrate method feasibility: strawberry, wheat grain, corn meal, rat urine, and E

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Figure 4. Hexazinone MS/MS quantitative analysis in corn meal, rat urine, and canola seed extracts that were spiked at 1.0 ng/mL (panels a, b, and c) and 5.0 ng/mL (panels d, e, and f). Raw data ion chronograms (before binning) for m/z 253 → m/z 171 are shown in panels a and d, where a 1.0 ng/mL hexazinone standard in reagent blank (black dots) is shown for comparison. The corresponding Am vs Snorm plots are shown in linear scale in panels b and e and logarithmic scale in panels c and f. Second order exponential regression analysis was used. Open circles correspond to data from the front of the ion chronogram peak including the apex, while filled circles are from the peak tail.

Figure 5. Quantitative analysis by linear regression, ln Am vs Snorm, for hexazinone at 5.0 ng/mL in rat urine (top, a and b) and canola seed (bottom, c and d).

distortions observed in FIA/MS/MS with real-time infinite dilution are currently under further investigation. Triflusulfuron methyl and flupyrsulfuron methyl (sulfonylurea herbicides) were also measured along with hexazinone in this

hexazinone in canola seed suggests that surface/matrix interactions during sample band transport were either negligible or the resulting analyte/matrix separation did not significantly affect A0 determinations. Split signals and asymmetrical signal F

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Table 3. Comparison of the Proposed Method (FIA/MS/MS with Real-Time Infinite Dilution) To Well-Established Techniques by Analysis of Strawberry Samples That Contained Residues of the Insecticide Chlorantraniliprole Field Sample Results, 3 Different Methods sample type

sample id Strawberry Strawberry Strawberry Strawberry Strawberry Strawberry

A B C D E F

control treated treated control treated treated

neat standards, HPLC/MS/MS (mg/kg, ppm)d,e

FIA/MS/MS with real-time infinite dilution (mg/kg, ppm)a,b,c n.a.g 0.19 ± 0.01, 0.17 ± 0.26 ± 0.04, 0.20 ± n.d.g 0.22 ± 0.01, 0.23 ± 0.20 ± 0.01, 0.24 ± Fortified Sample

n.d.g 0.19 0.21 n.d.g 0.01 0.24 0.01 0.21 Results, FIA/MS/MS with Real-Time Infinite Dilution 0.01 0.05

matrix-matching, FIA/MS/MS (mg/kg, ppm)d,f n.d.g 0.20 ± 0.26 ± n.d.g 0.24 ± 0.27 ±

0.01 0.01 0.03 0.01

sample id

sample type

mg/kg, ppmb,c,e

accuracy (%)

D + 0.010 mg/kg D + 0.20 mg/kg D + 4.00 mg/kg

fortified fortified fortified

0.010 ± 0.001 0.18 ± 0.01 3.58 ± 0.12

100 90 90

a

Duplicate analysis. bSecond order exponential regression used. cUncertainty covers 95% confidence interval. dLiterature data (ref 22). eSingle analysis. fTriplicate analysis reported as average ± standard deviation. gn.d. = not detected, n.a. = not analyzed.

Figure 6. Nonlinear regression results obtained for chlorantraniliprole (m/z 484 → m/z 453) in strawberry sample E-2. Top panels: (a) results from first order exponential regression and (b) corresponding residuals. Bottom panels: (c) results from second order exponential regression and (d) corresponding residuals. The obtained A0 results are presented to four decimal places to show the difference between the two models. Also, for assessment of regression model performance, the residual plots have been zoomed to ±10% of A0. The second order exponential regression (eq 12) performed better when strong matrix effects were encountered, as shown in this example. Consequently, chlorantraniliprole residues in strawberry field samples were quantified using the second order exponential regression. An increase in measurement uncertainty upon online sample dilution can also be seen in the residual plots due to decreasing signal-to-noise ratio.

and 96 ± 10 when eq 11 (Table S-3 in the Supporting Information) and eq 12 (Table S-4 in the Supporting Information) were used, respectively. The performance of both regression models was adequate and comparable to current quantitative mass spectrometry methods;25−27 accuracy between 80% and 120% and standard deviation triflusulfuron methyl > flupyrsulfuron methyl > chlorantraniliprole. Nevertheless, the resulting Am vs Snorm data are fitted well by the second order exponential functions in Figure 7b,d. The most responsive analyte (hexazinone) at 500 ng/mL in blood extract highlighted the applicability range of this method since it yielded a measurement accuracy of 78.2% (Figure 7c,d), which is just below the acceptable 80%. An additional experiment was performed with hexazinone in rat blood extract to elucidate the method applicable concentration range for the most sensitive analyte. This was determined to be 0.01 ng/mL to 100 ng/mL, as shown in Figure 7e and Figure S-7 in the Supporting Information, which is much wider than 0.01 to 5 ng/mL obtained for the conventional peak height vs concentration shown in Figure 7f. Quantitative methods that are applicable over wide concentration ranges are desired in chemical analysis as they reduce the need for dilution steps during sample preparation. Fast and Comprehensive Assessment of Matrix Effects. A comprehensive assessment of matrix effects is intrinsically provided by the method in addition to accurate quantitation despite matrix type and/or detector saturation. The matrix effect, ME, is a function of Snorm based on the following equation (see the Supporting Information for derivation of eq 15): ME(Snorm) =

A m (Snorm) A0

Then, merging eqs 11 and 12 with eq 15 results in ME(Snorm) = eb(Snorm)

(16)

and ME(Snorm) =

a ·eb(Snorm) + c·ed(Snorm) a+c

(17)

for the first and second order exponential models, respectively. Note that, as expected and for validation, the mathematical expression initially introduced in eq 5, limSnorm → 0+ME(Snorm) = 1, holds true in eqs 16 and 17.29 The ME function associated with each analyzed sample is elucidated when a, b, c, and d are revealed by curve fitting. In cases where the Am(Snorm) function is determined by first-order exponential regression analysis, the b parameter dictates the magnitude, direction, and decay of matrix effects by itself. In those cases, the matrix effects function will result in matrix suppression (ME < 1) when b < 0 and matrix enhancement (ME > 1) when b > 0. Absence of matrix effects should result in b = 0, which yields ME = 1. Figure 8 shows theoretical ME functions for b values ranging from −10 to 10 in order to illustrate the impact of the matrix effects index, b, on the ME function from eq 16. Under detector saturation conditions, the ME functions elucidated by this method reflect the combined effects of matrix and high analyte concentration on (i) analyte ionization at the ion source and (ii) ion manipulation and detection inside the mass spectrometer.

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CONCLUSIONS In essence, this quantitative analysis method can be described as a comprehensive titration of matrix effects by highthroughput FIA with measurements made at the infinite dilution limit. This was demonstrated for the example case of electrospray ionization/mass spectrometry. The method represents a practical solution around the matrix effects problem in quantitative analytical chemistry as well as an approach to study matrix effects phenomena with unprecedented speed and comprehensiveness. This method should expand the capability of MS (and potentially other techniques) with remarkable method simplicity. The known sensitivity improvement trend in analytical instrumentation30 will allow sample dilution of an even greater magnitude with newer mass spectrometers, providing an excellent outlook for this method. Development of software for automation of data processing

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described in this paper, which were practical across the systems, normalized sample concentration range, and experimental conditions tested. This observation qualitatively agrees with reports of matrix effects reduction as a function of sample dilution (see refs 7, 9, and 24). (24) Nanita, S. C.; Stry, J. J.; Pentz, A. M.; McClory, J. P.; May, J. H. J. Agric. Food. Chem. 2011, 59, 7557−7568. (25) Nováková, L. J. Chromatogr., A 2013, 1292, 25−37. (26) Botitsi, H. V.; Garbis, S. D.; Economou, A.; Tsipi, D. F. Mass Spectrom. Rev. 2011, 30, 907−939. (27) Wang, J.; Chow, W.; Leung, D.; Chang, J. J. Agric. Food Chem. 2012, 60, 12088−12104. (28) The method LOQ of 0.01 mg/kg is well below the 1.0 mg/kg maximum residue limit of chlorantraniliprole in strawberries (http:// www.mrldatabase.com). (29) Mathematical definitions of matrix effects and corrective approaches have been discussed in the literature (e.g., refs 6, 7, and 9) mainly to address the problem in absorption/emission spectrometry and chromatography/mass spectrometry. The mathematical considerations and equations described here have been presented to support the proposed FIA/MS method and provide a mathematical foundation for future work. (30) Thomson, B. Genetic Eng. Biotechnol. News 2012, 32, 20.

should reduce the time needed for data analysis and expedite method implementation.

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ASSOCIATED CONTENT

* Supporting Information S

Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 1-302-451-0031. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Dedicated, in appreciation, to Prof. Ingrid Montes, Prof. Osvaldo Rosario, and the chemistry faculty at the University of Puerto Rico-Rı ́o Piedras. The author thanks Joseph P. Klems, Mary Ellen P. McNally, and Barbara S. Larsen (DuPont Co.) for reviewing this manuscript and providing feedback prior to publication. Helpful discussions with Peter Stchur, Steve Cheatham, Melissa Ziegler, and John W. Green (DuPont Co.) are also acknowledged.

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REFERENCES

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dx.doi.org/10.1021/ac402567w | Anal. Chem. XXXX, XXX, XXX−XXX