Correction for Isotopic Interferences between Analyte and Internal

NMS Laboratories, 3701 Welsh Road, Willow Grove, Pennsylvania 19090, United States. § Department of Pathology, University of Utah School of Medicine,...
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Correction for Isotopic Interferences between Analyte and Internal Standard in Quantitative Mass Spectrometry by a Nonlinear Calibration Function Geoffrey S. Rule,† Zlatuse D. Clark,† Bingfang Yue,‡ and Alan L. Rockwood*,†,§ †

Institute for Clinical and Experimental Pathology, ARUP Laboratories, 500 Chipeta Way, Salt Lake City, Utah 84108, United States NMS Laboratories, 3701 Welsh Road, Willow Grove, Pennsylvania 19090, United States § Department of Pathology, University of Utah School of Medicine, 2100 Jones Medical Research Bldg., Salt Lake City, Utah 84132, United States ‡

S Supporting Information *

ABSTRACT: Stable isotope-labeled internal standards are of great utility in providing accurate quantitation in mass spectrometry (MS). An implicit assumption has been that there is no “cross talk” between signals of the internal standard and the target analyte. In some cases, however, naturally occurring isotopes of the analyte do contribute to the signal of the internal standard. This phenomenon becomes more pronounced for isotopically rich compounds, such as those containing sulfur, chlorine, or bromine, higher molecular weight compounds, and those at high analyte/internal standard concentration ratio. This can create nonlinear calibration behavior that may bias quantitative results. Here, we propose the use of a nonlinear but more accurate fitting of data for these situations that incorporates one or two constants determined experimentally for each analyte/internal standard combination and an adjustable calibration parameter. This fitting provides more accurate quantitation in MS-based assays where contributions from analyte to stable labeled internal standard signal exist. It can also correct for the reverse situation where an analyte is present in the internal standard as an impurity. The practical utility of this approach is described, and by using experimental data, the approach is compared to alternative fits.

Q

Use of nonlinear, or quadratic, curve fitting for calibration in both bioanalytical and clinical chemistry fields is not generally condoned or accepted.3 In the context of this paper, when the term “nonlinear” is used, it refers to nonlinearity of the calibration curve with respect to an independent variable, that is, nonlinear with respect to analyte concentration. The terms “nonlinear” and “quadratic” are often considered synonymous, but in this paper, we emphasize that the two be considered distinct. In particular, although all quadratic equations are nonlinear, not all nonlinear equations are quadratic, and for important classes of calibration data, certain nonquadratic nonlinear equations may appropriately be used as calibration functions. In this paper, “calibration” is taken to mean calibration for quantitative analysis and not calibration of the m/z scale. The appearance of nonlinear calibration curve data is not uncommon, and the cause of this behavior is not always obvious. Several causes can account for it, including detector saturation, dimer/multimer formation,4 and an isotope effect.1

uantitative mass spectrometry (MS) often makes use of stable isotope-labeled (SIL) internal standards. Quantitation is based on the ratio between analyte and internal standard (IS) signals. ISs are used to correct for variations in sample preparation, injection, ionization, and instrument performance. The drawback of omitting an IS is reduced accuracy and precision. Although seldom explicitly stated, one often makes certain assumptions about calibration curves, in particular, that the analyte does not interfere with the IS and the IS does not interfere with the analyte. Although this is often a reasonable assumption, it is seldom strictly true, and we and others have noticed cases where such interferences are significant, particularly when one considers isotopic peaks.1,2 These effects can lead to a calibration relationship that is nonlinear or that has a nonzero intercept. When there is a contaminant in the IS that interferes with the analyte, it produces a nonzero intercept. We refer to this as “contaminant interference” (CI). The case where an analyte isotope interferes with the IS produces nonlinearity. We refer to this as “isotope to IS interference” (IISI). These two effects can occur either singly or in combination, depending on the system under consideration. © 2013 American Chemical Society

Received: October 23, 2012 Accepted: March 7, 2013 Published: March 12, 2013 3879

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“Self-suppression”, or reduced ionization efficiency at higher analyte concentrations, can be a cause when using an analogue IS but is not generally an issue when coeluting SIL ISs are used.5 At times, nonlinear behavior may create obvious quantitative biases when choosing a linear fit, and it may limit the dynamic range for the assay. At other times, the bias may be less obvious but present nevertheless. A general awareness of these effects exists in some analytical laboratories, and they have been reported in the literature.1,2,6 Recently Tan et al.7 provided a more thorough analysis of these influences on curve linearity by varying IS amount and isotopic contribution levels using d9-tiagabine to simulate an isotope effect. In that work, the effect of alternative weighted linear fits are compared to an unweighted fit to illustrate the extent of bias in situations where varying degrees of isotope effect are present. The influence of CI is also detailed. However, to our knowledge, no one has explicitly presented the governing equations for these effects or shown how to use these equations for calibration. Rather than fitting some arbitrarily chosen nonlinear calibration function to a set of calibration data, our approach here is based on mathematical equations deriving from a realistic physical model and properties that can be experimentally determined for each analyte/IS pair. Industry guidelines generally help to control the extent of these effects.8 In the bioanalytical setting, a recommendation may be made to limit the contribution from an analyte isotope to the IS signal to 5% or less at the highest concentration. In effect, this measure may require use of higher than desirable IS concentrations, due to CI, or limiting the dynamic range of the assay. In the clinical chemistry setting, it is not unusual to have assays that use relatively low concentration calibrators for daily analysis and to use a linear extrapolation for quantitation to a higher analyte concentration.9 In this scheme, the full range, including the extrapolated region, is known as an analytical measurement range (AMR). Reasons for extrapolation in this fashion may be due to a limited number of samples falling in the upper regions of the desired range, a desire to limit the number of calibrators used, or because of issues related to carryover. Furthermore, inclusion of higher-concentration calibrators may produce greater error in the low-concentration region of the calibration line, either through statistical variability or as a result of an underlying nonlinear calibration relationship. However, the result of a linear extrapolation can be a systematic quantitative bias at higher levels resulting from IISI. These circumstances are not always under laboratory control, and for example, it may be necessary to use a less ideal IS or concentration due to cost, availability, and purity. In other situations, ISs that are highly labeled with deuterium may suffer chromatographic separation from the analyte itself10 thus detracting from their usefulness, or with endogenous compounds, interferences may exist that limit the choice of IS to one that is less desirable in other ways. Furthermore, in cases where both IISI and CI exist, one can change the IS concentration to reduce the extent of one interference only at the expense of increasing the other. In some cases, a quadratic fit may be contemplated for nonlinear data, but it should be noted that this is at a fairly fundamental level an improper fit, since it is parabolic if taken to very high concentrations and has the wrong asymptotic behavior. Alternatively, linear fits may be chosen with some form of weighting to provide better accuracy (on a compromise basis) across the range of interest. In this case, it may be

observed that high concentrations are consistently biased low. This may be accepted so long as the deviation from the regression line is not too significant. Here, we show how two simple equations can be used to provide a more accurate fit to isotope-caused, nonlinear MS data. These equations use one or two experimentally determined constants and a single adjustable parameter determined for each set of calibration points. These equations can be used to correct for both the IISI as well as the offset that occurs in the y intercept from CI (in some cases CI may be due to background interference that exists with endogenous compounds in some matrices). We show how the fit can be used to correct for IISI and provide improved quantitative results over those obtained by a strict linear fit.

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METHODS

Computations were done using PSI-Plot (version 10, Poly Software International, Pearl River, NY) with user defined equations and the built-in Levenberg−Marquardt dampened least-squares algorithm for determination of adjustable parameter A defined in equations below. Reference materials hydroxytriazolam (HTRZ), estradiol, and internal standards (d4-HTRZ and d3-estradiol) were purchased from Cerilliant (Round Rock, TX) or CDN Isotopes (Pointe-Claire, Quebec, Canada), respectively. Solvents were purchased from J.T. Baker, and water was prepared in-house using an 18 MΩ resin purification system. Formic acid and dansyl chloride were from Fluka (Sigma−Aldrich, St. Louis, MO). Two methods currently employed in our laboratory were selected for this investigation based on observed or predicted nonlinear behavior: one for a determination of estradiol, and the second for a benzodiazepine (HTRZ). For estradiol, the assay calibrators are placed at 5, 20, 50, 80, 120, and 200 pg/mL serum. In our laboratory, the analytical measurement range is extended up to 2000 pg/mL, but here, we evaluated additional test samples up to 4000 pg/mL. The IS is used at a concentration equivalent to 200 pg/mL serum. Estradiol was extracted from control serum using methyl t-butyl ether extraction followed by derivatization with dansyl chloride. The dansylation reaction was carried out by combining equal volumes of a solution of dansyl chloride (1 g/L) with 10 mM sodium carbonate buffer and adding 50 μL of this solution to each sample well of a 96-well plate. The plate is covered and then incubated at 70 °C for 10 min. A reconstitution solution of 1:1 water/acetonitrile (50 μL) is then added prior to injection. The method and analysis of estradiol were performed using a column switching system identical to that described by Kushnir et al.11 Our normal calibration range for HTRZ in urine covers 20− 200 ng/mL with the AMR extended up to 5000 ng/mL. A d4-IS is used at a concentration equivalent to 100 ng/mL in urine, or 2% of the upper concentration limit. For our experiments, we prepared calibrators at seven concentrations of 0.25, 1, 2.5, 10, 25, 100, and 250 ng/mL, each in a solution of 75% water, 25% acetonitrile, and injected 20 μL on to the column. Concentrations were adjusted downward due to use of a more sensitive instrument for these studies than our standard laboratory assay. The d4- HTRZ IS was also used at 2% of the upper concentration limit or 5 ng/mL. The chromatographic conditions used for HTRZ were on a Waters XTerra MS C18 analytical column (2.1 mm × 150 mm) with 3.5 μm particle 3880

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representing the CI, depends on the purity of the IS resulting from a chemical synthesis. It is our experience that a small percentage of a SIL IS is commonly found to be without isotope labeling and will give rise to CI. With some substitution and rearrangement and defining a new parameter, A = F1/F4, we arrive at the following equation:

size and a generic gradient of acetonitrile and water, each containing 0.1% formic acid. Data were generated on an AB SCIEX Triple Quad 5500 LC/MS/MS System mass spectrometer using a Turbo Ionspray source in positive ion mode and within the linear response range of the detector (taken to be approximately 4 x106 cps). Transitions monitored for dansyl estradiol and d3-dansyl estradiol were from 506 to 156 and 171 and from 509 to 156 and 171 amu, while for HTRZ and d4- HTRZ, the transitions were from 359.3 to 176 and from 363.3 to 176 amu, respectively. Quantitation was done using Analyst software version 1.5.2.

R C T + A C I) ( R=A 0

(

A C R∞ T

)

+ CI

(3)

Here, A can be treated as an adjustable parameter that is determined at the time of calibration. This parameter may vary if, for example, different collision energies are used for the analyte and IS or if the IS concentration is varied. Equations 1 and 2 are linear functions of the analyte and IS concentrations. However, when one forms the ratio (R) between the two, the resulting function is a nonlinear function of the analyte and IS concentrations. This nonlinearity is inherent in a calibration scheme that uses the ratio R as a basis of quantitative analysis. An exception to this rule occurs if R∞ = ∞, in which case R is a linear function of the analyte concentration. Values for both R∞ and R0 are determined experimentally for each analyte/IS combination and for each lot of IS, respectively, as illustrated in Figure 2. R∞ is then the peak area ratio (R) determined when analyte is present but IS is not.

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RESULTS AND DISCUSSION We wanted to develop a regression equation that would allow us to provide a more accurate fit to quantitative data in situations where a SIL IS is used but where IISI exists. We also wanted to consider an additional, optional, adjustment for a CI. While we generally think of tandem MS and a specific precursor/product ion combination, as being the method of choice for much quantitative MS, we wish to point out that this approach may be used for single-stage MS analysis as well. Consider the situation, shown in Figure 1, where there are contributions to ion intensities of interest (IT and II), for both the target and the IS, respectively.

Figure 1. Depiction of contributions to target ion intensity (IT) and IS ion intensity (II) from the target analyte M + 0 isotope (F1), a heavy isotope (F2), unlabeled impurity in IS (F3), and heavy labeled IS (F4).

Here, F1 and F2 represent the relative contributions of the M + 0 precursor (analyte) and the relevant heavy isotope to the product ion(s) of interest, respectively. F3 and F4 are the relative contributions from CI and the labeled IS, respectively. In Figure 1, we illustrate IT and II as being of different masses, but in some cases, the product ions selected may be the same mass. For the ion intensities of target analyte and IS masses, we then have

IT = FC 1 T + F3C I

Figure 2. Extracted ion current chromatograms illustrating the contribution to the IS transition (solid fill) from the M + 3 isotope of analyte but in the absence of IS. The flat top on the m/z 506 to 171 transition indicates off-scale intensity, not detector saturation.

The ratio of the signals (analyte transition/IS transition, measuring F1/F2) gives R∞. R0 is determined in a similar fashion, monitoring the same two transitions, but injecting labeled IS without added analyte. With a set of calibration data points, utilizing both analyte and IS, along with values for R∞ and R0, one can solve for parameter A. A may be determined either by use of nonlinear least-squares regression fitting, or by solving eq 4 for A at several concentrations and determining a representative value for A from the resulting set of values, for example, the median or the mean of the set of values, or some other estimate of the best value for A:

(1)

and II = F2C T + F4C I

(2)

where CT and CI are the respective concentrations for the target analyte and the IS. Correcting for extraction and other process variation, by use of the IS, the peak area ratio used for quantitation is then IT/II, which we simplify as R. We also define a constant R∞ as equal to F1/F2 and a constant R0 as equal to F3/F4. Note that the former, from IISI, is determined by the composition, structure, and fragment selected for the analyte, while the latter, 3881

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A=

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(R 0 − R )C I

(

CT

R R∞

)

−1

R= (4)

(R 0 − R )C I A

(

R R∞

)

−1

(

)

+ CI

(6)

As noted above, R∞ can be determined experimentally by measuring R in a sample containing analyte but no IS, and this is the approach used for data analysis in the present paper. However, it is also possible to estimate R∞ using theoretical methods. In a single-stage MS experiment, F2, and hence R∞, is determined solely by the abundance of the analyte isotope corresponding to the mass of the IS. In quantitative tandem MS, however, the IISI contribution also depends on the fragment ions being monitored and on the size and composition of the fragment in relation to the precursor molecule. This principal has been described previously by Bozorgzadeh et al.12 in looking at small molecule fragmentation, by Singleton et al.13 examining halogenated compounds, and by O’Connor et al.14 for determining the isotope content of selected ubiquitin precursor ions from their fragmentation spectra. The information contained within product ion spectra was further elaborated upon by Rockwood et al.15 where a fully general algorithm was developed for prediction of fragment isotope distributions from any given precursor isotope. The use of this distribution information in determining fragment structure and composition was also illustrated. More recently, Ramaley and Herrera6 developed and provided a software program for computing theoretical fragment ion distributions from a given precursor isotope. Since the IISI is not always obvious based on examination of the precursor isotope distribution alone, we provide some discussion of the probability-based, heavy isotope distribution of fragment ions with the Supporting Information.

Once A has been determined for a given set of conditions (mass spectrometer, reference standards, and IS concentration), it is possible to solve CT for any given value of R generated from an unknown sample using eq 5:

CT =

AC T A C R∞ T

(5)

A simulated example of the IISI when taken to high analyte concentration using eq 3 is shown as the “true curve” of Figure 3.

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Figure 3. Plot illustrating IISI effect on curve shape, taken to high concentration extreme. Curves are for an example compound with R∞ = 200, R0 = 0, A = 1, and CI = 75 (arbitrary concentration units). The linear fit illustrates in exaggerated fashion the relationship to “true” data where IISI exists.

EXAMPLE 1 For estradiol quantitation in our laboratory, the AMR covers 1−2000 pg/mL. Calibrators for each batch span the range 5− 200 pg/mL, and IS is added at a concentration of 200 pg/mL. When it is necessary to analyze a sample whose concentration is above that of the highest calibrator but lower than the upper limit of the AMR, the calibration curve is extrapolated outside of the range covered by the calibrators. Necessary conditions for this to be valid are that the extrapolated calibration curve must be well-behaved and be of a functional form that gives a good representation of the data. To obtain the highest sensitivity for this assay, we make use of a dansyl derivative (Figure 4). The sulfur-containing dansyl

As seen, the use of a linear fit in this situation results in a negative bias at both high and low concentrations and a positive bias in the intermediate regions of the curve. The asymptote, R∞, shows the limit that peak area ratio will approach as analyte concentration gets very high and its influence on apparent IS peak area, resulting from IISI, dominates. The use of a quadratic fit in this situation is not of the correct form as it would reach a maximum value of R and then descend or conceivably deflect upward through and beyond the asymptote. That is, a quadratic will approach either positive or negative infinity as the concentration increases, rather than approaching an asymptotic value. The “ideal” linear fit shown would occur in a situation with no isotope effect and have a slope equivalent to the tangent at CT = 0. In practice, the effect of utilizing higher IS concentrations serves to force the value of R to lower regions of the curve where the nonlinearity is not as extreme. A positive value of R0, due to CI, equates to a nonzero value for the y intercept in the calibration plot. In many situations, the level of the CI, in addition to autosampler carryover, is managed so as to contribute only a small percentage (generally ≤20%) to the lowest calibration standard. This may be performed in part by limiting the concentration of the IS used. In this, or similar situations where CI is negligible, eq 3 can be simplified as shown in eq 6. The two examples we present below make use of this simplified form:

Figure 4. Dansylated estradiol showing position of deuterium atoms on the IS and the two most abundant fragment ions. 3882

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moiety contributes a relatively large M + 2 isotope (34S has an average of 4.21% of 32S abundance) to the compound. Together the naturally occurring heavy isotopes of this compound combine to yield an M + 3 contribution of 2.5% that of the M + 0 component. For the data analysis in this paper, we used a value of R∞ determined experimentally using a method discussed in an earlier section of this paper. With an R∞ value of 79 and setting R0 = 0, we used eq 4 with data from a set of calibration standards (at 5, 20, 50, 80, 120, and 200 pg/mL) to generate a mean value of A of 1.075. This value was then used with eq 3 to generate ideal peak area ratios (R) shown extended across the concentration range of interest as the solid line in Figure 5. An

Table 1. Percent Accuracy as Determined by Two Fitting Approachesa A conc (pg/mL)

nonlinear accuracy (%)

linear accuracy (%)

80 200 400 800 1600 2400 3200 4000

98.7 98.0 102 101 102 103 105 103 B

101 99.9 103 99.3 95.0 91.2 88.2 83.1

conc (pg/mL)

nonlinear accuracy (%)

linear accuracy (%)

5 20 50 80 120 200

106 105 95.2 100 94.2 99.0

96.1 106 97.3 103 96.7 101

a

(A) Mean of two replicate determinations of the test samples evaluated by both linear and nonlinear calibration, including highconcentration samples beyond the 200 pg/mL upper limit of the calibrators. (B) Back-calculated accuracy for each of individual calibrators used to generate the parameters for each regression approach. In both cases, percent accuracy is determined as the concentration calculated from the regression line divided by theoretical concentration.

Figure 5. Dansyl estradiol example: comparison between an extrapolated linear regression (dashed line) with the extrapolated nonlinear fit (solid line). Calibration standards used to determine the regression parameters in each case extend up to 200 pg/mL as shown in the inset. The individual points shown in the main plot are from a set of test samples that was not used for either regression fitting of the calibrators. Figure 6. Structure of HTRZ showing the position of deuterium atoms on the IS.

unweighted linear regression was used with the same calibration standards to generate the dashed line shown extrapolated to the upper quantitation limit. A separate set of samples was analyzed at the same time, using eight concentrations each in duplicate and the concentrations calculated from both the linear equation and according to the nonlinear fit of eq 5 (Table 1.) Figure 5, along with Table 1A, shows the accuracy obtained with our nonlinear fit, in comparison to a linear one, after extrapolation beyond the upper calibration standard (200 pg/ mL) in each case. Table 1B shows accuracy values obtained for each case with the calibration standards themselves. This data suggests that, in such cases, it is possible to remove some of the systematic bias that occurs with high concentration quantitation, when IISI exists and where a regression is extrapolated beyond the level of the daily calibration standards. The nonlinear calibration relation gives very good accuracy, both within and outside of the calibration range, whereas the linear calibration relationship fails to give an accurate result at the higher concentrations.

In this case, the compound contains two chlorine atoms giving a substantial M + 4 peak (12% of monoisotopic mass) at the same mass as the d4-IS utilized for this assay. Separate experiments determined that the fragment ion utilized for quantitation (mass of 176 amu) bears one chlorine atom but none of the deuterium atoms. An experimental determination of R∞ (203) provided the nonlinear fit to calibration data as shown in Figure 7, with an A parameter of 0.8487. For comparison, both weighted and unweighted linear fits are shown. In this example, we treated the data without extrapolation, as one would do for a bioanalytical analysis, though with a relatively low IS concentration. All levels of calibration standards, each in duplicate, were used for regression. For each regression type, back-calculated concentrations were generated for each calibration level across the quantitation range. As seen in Table 2, the use of an unweighted linear fit does not suffice across the 1000-fold concentration range of this example, due to the nonlinearity of the data. The y intercept is pulled exceedingly high resulting in nonreportable (negative) values of concentration at the low end of the curve.

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EXAMPLE 2 In a second example, we examined the influence of IISI on curve linearity for HTRZ, a compound in the benzodiazepine class. The structure of this compound is shown in Figure 6. 3883

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Information, we provide a lookup table illustrating such a figure. It is seen that compounds with R∞ values of 40 000 will tolerate extremely low IS concentrations without significant influence on linear quantitation. At the other extreme, compounds with very low R∞, require very high IS concentration to minimize IISI. We suggest that the R∞ value should be determined early during method development and an estimate of nonlinearity made from the table. The approach suggested in this paper could be classed as a “model-driven” calibration strategy. By this we mean that we start with the underlying physical properties of the system and the realization that isotopic peaks from the analyte may interfere with the IS and vice versa. When the ratio is taken between the analyte and IS peaks, the physical model predicts that the calibration equation is constrained to a specific functional form. The calibration data, which may include the separate determination of some parameters, is then used to calculate the parameters in the calibration equation. Determination of the actual calibration parameters in a given case is therefore “data driven.” A risk to our approach is that, if the physical model on which the calibration relationship is based is incorrect, then the calibration function may be of the wrong form. This is in contrast to a “data driven” approach, in which calibration data are used to determine parameters in a calibration equation that is of very general functional form but not necessarily based on the physics of the analytical system. We also note that, because the parameters R∞ and R0 can be determined with high accuracy, all the statistical power of a set of calibrators in a run is concentrated into providing the best value for a single adjustable parameter, A, rather than being diluted into providing values for two parameters, a slope and intercept. Thus, in our view, this alternative calibration strategy has potential to provide better precision as well as better accuracy in many cases. Finally, the discussion in this paper is not meant to deal with all sources of nonlinearity. It does not deal with the problem of detector saturation. In the latter situation, or if other forms of nonlinearity occur, then the methods in this paper cannot be directly applied. If possible, one should deal with the other causes of nonlinearity before applying the methods presented here. The isotope effects described will occur regardless of the type of mass spectrometer or ionization source used, although the extent of the effect may be reduced with tandem MS and fortuitous fragmentation and IS labeling.

Figure 7. Plot of HTRZ data showing nonlinear regression (solid line), the 1/X2 weighted linear regression (upper dashed line), and unweighted linear regression (lower dashed line). In the inset, the relative position of the two linear fits is reversed, i.e., the upper dashed line is unweighted.

Table 2. Comparison of Back-Calculated Accuracy Values for HTRZ with Use of Various Fitting Options

r value std 1, 0.25 ng/mL std 2, 1 ng/mL std 3, 2.5 ng/mL std 4, 10 ng/mL std 5, 25 ng/mL std 6, 100 ng/mL std 7, 250 ng/mL

linear (unweighted)

linear (1/X weighting)

linear (1/X2 weighting)

nonlinear

0.9988

0.9979

0.9973

0.9998

no value

59.5

98.3

107

no value

104

106

104

22.6

109

104

100

96.3

114

106

101

107

111

102

99

109

107

97.8

100

98.5

95.6

87.4

99.9

Use of a 1/X weighted fit improves the quantitation at low concentrations, although the dynamic range is still limited by inaccuracies at lower concentrations. A noticeable positive bias is also seen at intermediate concentration levels. The 1/X2 weighting further pulls the fit toward more accurate values at the lower, linear region of the curve. However, accuracy is now beginning to degrade at the higher concentrations, nearly approaching an unacceptable limit of 15% error. In this case, we would expect that a relatively high proportion of analytical runs may fail due to excessive deviation at the highest calibration concentration. In addition, any sample determinations reported from the high end of the range in this situation would be biased low. The root-mean-square (rms) percentage error of the seven data points is 6.4% In contrast with the linear calibration relations, the nonlinear calibration produces good accuracy over the full concentration range studied. The r value (0.9998), the rms percentage error (3.1%), and the maximum error (7%) are all superior to any of the linear fits. We suggest that a simple figure of merit can be utilized to compare the likely extent of nonlinearity with different analyte/ IS combinations and method scenarios. In the Supporting

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CONCLUSION We have illustrated how a simple equation and experimental determination of two constants, together with one adjustable calibration constant, for specific compound/IS combinations, can be used to eliminate the inherent bias that exists in quantitation where IISI occurs. In our experience, it is not uncommon to see calibration curves with negative deviations at either the high or low ends, or both depending on the degree of weighting used, and positive deviations occurring through the middle of the range. This is often the result of a linear fit being forced onto nonlinear data. In such cases, an adequate linear fit may sometimes be achieved by keeping the IS concentration relatively high in relation to the highest analyte concentration. However, this situation may still result in some systematic bias depending on the fit and dynamic range used. We also suggest that the effects discussed in this paper are often overlooked by investigators and likely limit the dynamic range of many assays. 3884

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Truog, J.; Hussain, S.; Lundberg, R.; Breau, A.; Zhang, T.; Jonker, J.; Berger, N.; Gagnon-Carignan, S.; Nehls, C.; Nicholson, R.; Hilhorst, M.; Karnik, S.; de Boer, T.; Houghton, R.; Smith, K.; Cojocaru, L.; Allen, M.; Harter, T.; Fatmi, S.; Sayyarpour, F.; Vija, J.; Malone, M.; Heller, D. Bioanalysis 2011, 3 (12), 1323−32. (9) CLSI, Mass Spectrometry in the Clinical Laboratory: General Principles and Guidance; Approved Guideline; Clinical and Laboratory Standards Institute: Wayne, PA, 2007. (10) Kato, K.; Jingu, S.; Ogawa, N.; Higuchi, S. J. Pharm. Biomed. Anal. 2000, 24 (2), 237−49. (11) Kushnir, M. M.; Rockwood, A. L.; Yue, B.; Meikle, A. W. Methods Mol. Biol. 2010, 603, 219−28. (12) Bozorgzadeh, M. H.; Morgan, R. P.; Beynon, J. H. Analyst 1978, 103, 613−22. (13) Singleton, K. E.; Cooks, R. G.; Wood, K. V. Anal. Chem. 1983, 55, 762−4. (14) O’Connor, P. B.; Little, D. P.; McLafferty, F. W. Anal. Chem. 1996, 68 (3), 542−5. (15) Rockwood, A. L.; Kushnir, M. M.; Nelson, G. J. J. Am. Soc. Mass Spectrom. 2003, 14 (4), 311−22.

In some cases, a CI produces a substantial, undesirable contribution to the LLOQ, and high IS concentrations can suppress analyte ionization influencing the LOQ level achievable. The utility of the nonlinear approach presented here is that these considerations may be eliminated. The IS can be utilized at lower concentrations and without regard to IISI. This may allow use of ISs with a limited degree of mass labeling, such as d2 for example, and quantitation over a broader dynamic range than might otherwise be achievable with linear fits. There are several limitations related to use of the approach suggested. It is conceptually more complex than a linear fit, and it does not take into consideration all possible sources of nonlinearity. In addition, current commercially available data systems do not typically accommodate the inclusion of such user defined fits, the response of regulatory agencies cannot be known at the present time, and consensus on requirements for validation or revalidation does not yet exist. However, as a minimum, it would seem prudent to revalidate R∞ and R0 with each new lot of reagents. Finally, it is possible that precision may suffer slightly were the fit to be used in the extreme nonlinear region. However, we believe the improvement in the quantitative accuracy provided by this calibration approach outweighs any minor increase in imprecision in the high concentration range. We plan to more fully characterize these issues in future validation efforts.

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on March 29, 2013. An abstract graphic was added, and the corrected version was reposted on April 16, 2013.

ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in the text. 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]; fax: 801-584-5048. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank ARUP Institute for Clinical and Experimental Pathology for supporting this project. REFERENCES

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dx.doi.org/10.1021/ac303096w | Anal. Chem. 2013, 85, 3879−3885