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Cite This: Anal. Chem. XXXX, XXX, XXX−XXX

Development, Validation, and Application of a New Method To Correct the Nonlinearity Problem in LC-MS/MS Quantification Using Stable Isotope-Labeled Internal Standards Qian Liu,†,§,∥ Fulin Jiang,†,∥ Janshon Zhu,‡ Guoping Zhong,*,† and Min Huang*,† †

School of Pharmaceutical Sciences, Sun Yat-sen University, Guangzhou 510006, Guangdong Province, China Guangdong RangerBio Technologies Co., Ltd., Dongguan 523000, Guangdong Province, China § The Second Affiliated Hospital of Guizhou Medical University, Kaili 556000, Guizhou Province, China Downloaded via NOTTINGHAM TRENT UNIV on July 17, 2019 at 07:04:19 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: Liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) has become an indispensable tool for bioanalysis. To quantify a small molecule with LC-MS/MS, a stable isotope-labeled analyte is routinely used as the internal standard. However, cross signal contributions between the analyte and its stable isotope labeled internal standard (SIL-IS) could cause problems when the signal response of the LC-MS/MS system is nonlinear. In the present work, we try to illustrate how the “cross talk” between the analyte and its SIL-IS may cause problems for a nonlinear system. We assume that the instrumental responses toward the analyte and its SIL-IS are the same. When the calibration curve is nonlinear, the addition of a SIL-IS would practically move the response of the analyte up along the parabolic line causing a change in the signal strength of the analyte (usually decrease). The more the SIL-IS is added, the larger change the analyte signal would become. Such a problem would only be corrected by making the calibration curve linear. To this end, we proposed a component equation (CE) as the calibration for nonlinearity correction. In this study, we contrasted the accuracy of CE with the common quantitative method using two drugs whose mass spectrometric responses are linear and nonlinear, respectively. The acceptable accuracy results demonstrated that the CE calibration was comparable with the regular quantitative SIL-IS method with a proper weighting factor and much better than that without weighting. Therefore, CE calibration may provide another reliable way for LC-MS/MS quantification.

W

source, is the atmospheric pressure ionization (API) source, including the electrospray ionization (ESI) and the atmospheric pressure chemical ionization (APCI) sources. Ionization in those ion sources is a dynamic controlled chemical reaction (M + H+ → [MH]+ or M − H+ → [M − H]−) with the reaction time in the millisecond range. Since the reaction rate highly depends on the molecular structure of the reagent and the reaction conditions, change of environment inside the ion source could have decisive effect on ionization efficiencies of different molecules. It is well-known that the same type of API source made by different manufacturers could yield quite different ionization patterns. Even the same ion source at different times or under different input flow conditions could produce different ions or ion patterns for a given sample. This leads to the necessity of using stable isotope-labeled internal standard (SIL-IS) in LC-MS/MS quantification simply because the chemical and physical properties of a SIL-IS is nearly

ith the increasing demand of precision and sensitivity in analysis, liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) becomes a dominant analytical technique for small molecule bioanalysis in pharmaceutical and biotech industries because of its high sensitivity and selectivity.1 However, in a LC-MS/MS system, the interior environment of LC and MS keeps changing, such as the mobile phase gradient flow, the column efficiency deterioration, the system temperature fluctuations, the ionization efficiency draft, the mass detector noise, and so on, internal standards are commonly used in LC-MS/MS quantification to compensate those variations as well as errors in sample preparation and injection.1−4 The ratio of analyte to internal standard (IS) signals is the base of quantification.4,5 It is assumed that, when a given amount of IS at a certain concentration is added to the samples, the peak area ratio of the analyte to the internal standard should remain constant at a specific analyte concentration, regardless of what may have occurred in the analytical process. However, the most commonly used interface between the liquid chromatograph and the mass spectrometer in a LC/MS system, that is, the ion © XXXX American Chemical Society

Received: February 20, 2019 Accepted: July 3, 2019 Published: July 3, 2019 A

DOI: 10.1021/acs.analchem.9b00947 Anal. Chem. XXXX, XXX, XXX−XXX

Article

Analytical Chemistry identical to the unlabeled analyte.2,6,7 Any different molecule used as the internal standard for LC-MS/MS quantification may work perfectly at one time or on one system at the best, but such a method would never guarantee transferability and repeatability. It has been commonly assumed that there is no interaction between analyte and its SIL-IS in LC-MS/MS quantification. We found the assumption untrue when the calibration is nonlinear. Several authors reported similar discoveries by looking into the change in SIL-IS peak area at different analyte concentrations.5,8,9 Previous research revealed that the peak area of SIL-IS decreases as the analyte concentration increases.8,10 Calibration with different SIL-IS concentrations would give different results for the same sample when the system response is nonlinear. The SIL-IS with an adequately high concentration even interacted with analyte due to chemical or isotopic interferences.11,12 Duxbury et al.8 reported that the calibration curve shows better and better linearity with higher and higher SIL-IS concentration. We encountered the same phenomenon in the present study. Some researchers briefly proposed criteria for choosing the proper concentration of IS without validating the influence of such choice on the accuracy and precision of the final analytical results. In this study, we compared the sensitivity and accuracy of SIL-IS methods with varying SIL-IS concentrations using two drugs whose mass spectrometry (MS) behaviors were nonlinear and linear respective within the calibration range. Moreover, many researchers have noticed that the utilization of a SIL-IS does not guarantee a successful bioanalytical method.2,13−15 Nonlinear calibration curves are very common in LC-MS/MS assays. The severity of nonlinearity could vary when running the same analyte on different days. The standard curves of the same analyte could be linear or nonlinear when run at different time or on different systems. To account for such phenomenon, quite a few explanations were proposed including saturation at high concentration during ionization,16,17 formation of dimer/multimer/cluster ions,18,19 charge competition,20 and detector saturation.18,21 In some cases, quadratic regression was employed to contemplate the nonlinearity.22,23 Although quadratic fitting can extend the dynamic range, it was not generally accepted in many regulatory analyses due to the quantitative biases. Such bias occurs mainly because of the calibration curve being parabolic at very high concentrations, and the wrongfully asymptotic behavior was introduced into the final analytical results.5 Consequently, quadratic regression is regarded to be improper and less desirable, especially for regulated analysis. Alternatively, better linearity may be achieved with a proper weighting factor incorporated in the regression across the range of interest. However, the choice of the weighting factor is highly arbitrary. There were many more efforts in seeking ways and means to improve calibration linearity. For example, Liu et al.24 and Trobbiani et al.25 provided an approach using less abundant isotopologue to reduce saturation at the detector and extend the linear range. There was also a graphical approach model attempted to eliminate the source of error in nonlinear calibrations.15 Rule et al. described two concepts in their paper,5 one was contaminant interference (CI), another was isotope to IS interference (IISI). Both CI and IISI can lead to nonlinearity. The authors further proposed two equations to fit the isotope-caused nonlinear MS data. However, all the proposed methods so far were to solve the nonlinearity problem without locating the causes behind it. By looking into

the problem with a series of experiments, we found that signals of mass spectrometer from both an analyte and its SIL-IS were almost the same in terms of sensitivity and responsive behaviors. Other than mass separation, both isotope-labeled and unlabeled analytes were seen as the same molecule by the mass spectrometer. This found led us to introduce a new quantitative model that we named it component equation (CE). Calibration with the CE model yielded well-improved linearity and avoided the quantitative bias existing in quadratic regression. In this paper, “nonlinear” refers to the nonlinearity of analyte responsive behavior, synonymous with “quadratic”. In this study, we analyzed two drugs, one responding linearly and the other nonlinearly within the calibration range. Their concentration ranges were set partially according to the literature26−28 and partially based on the needs for our following studies. We calibrated the data with the CE model as well as the different common regressions and compared the results. The accuracies resulted from CE calibration were comparable to or better than that from the commonly used calibration methods with various concentrations of SIL-IS. Our results validated that CE calibration provided an alternative quantification approach for an isotope internal standard method, particularly for nonlinear situations.

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EXPERIMENTAL SECTION Materials and Reagents. Metformin (99.9%), Omeprazole (99.9%), and Enalapril (99.9%) were purchased from the National Institutes for Food and Drug Control (Beijing, China). Metformin-d6 (99.9%) and Enalapril-d5 (99.8%) were purchased from Cato Research Chemicals Inc. (Oregon, U.S.). HPLC grade methanol and acetonitrile were obtained from Anhui Fulltime Specialized Solvents and Reagents Co., Ltd. (Anhui, China). Formic acid was purchased from Tianjin Kemiou Chemical Reagent Co., Ltd. (Tianjin, China). Deionized water was produced in-house by ELGA Purelab plus water system from the U.K. Standards were weighed using an electronic balance of 1/10000 from Sartorius (Gottingen, Germany). LC-MS Platform. All sample analyses were performed on a Agilent 1100 series liquid chromatogragh (LC) coupled with a Thermo Scientific LTQ-Orbitrap XL mass spectrometer (Thermo Fisher Scientific, Massachusetts, U.S.), which was controlled by Xcalibur 2.2 software. This software was also used for data acquisition and data processing. All the separations were achieved on a Thermo Hypersil GOLD analysis column (2.1 mm × 50 mm, particle size 1.9 μm). Metformin was run with isocratic elution using a mobile phase of 0.1% formic acid in water (40%) and acetonitrile (60%) at the flow rate of 0.25 mL/min. Enalapril was also run with isocratic elution using a mobile phase of 0.1% formic acid in water (30%) and methanol (70%) at the flow rate 0.30 mL/ min. The transition monitored for the Metformin, Metformin-d6, Enalapril, Enalapril-d5 and Omeprazole were m/z 130.2 → 60.1, m/z 136.2 → 60.1, m/z 377.3 → 234.2, m/z 382.5 → 239.2, and m/z 346.2 → 198.1, respectively. Stock Solutions and Sample Preparation. All stock solutions of the analytes and their internal standards (ISs) were prepared separately in methanol at 2.0 mg/mL. The standard solutions for eight calibration series were prepared in methanol. Each series contained eight concentration levels at 10.0, 20.0, 50.0, 100.0, 200.0, 500.0, 1000.0, and 2000.0 ng/ mL. The ISs whose concentrations were set to be 10.0, 20.0, B

DOI: 10.1021/acs.analchem.9b00947 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

Figure 1. LLOQ (10.0 ng/mL) response variation of Metformin with Metformin-d6 (A) or Omeprazole (B) as IS and Enalapril with Enalapril-d5 (C) or Omeprazole (D) as IS. The concentrations of IS were set to be from 10.0 to 2000.0 ng/mL. The relative standard deviation (RSD%) was calculated based on the response of LLOQ of each standard curve with eight different levels of IS. Each calibration series was prepared in duplicate.

Metformin (analyte) and Metformin-d6 (SIL-IS); Group 2 consisted of Metformin (analyte) and Omeprazole (NIS-IS); Group 3 consisted of Enalapril (analyte) and Enalapril-d5 (SILIS); and Group 4 consisted of Enalapril (analyte) and Omeprazole (NIS-IS). Different calibration standard series with different IS concentrations were prepared for each group. Calibrations for each standard series were done in the concentration range of 10.0−2000.0 ng/mL. We compared the changes in the analyte response with different IS concentrations from 10.0 to 2000.0 ng/mL and also the changes in the IS response at a fixed concentration with the change of calibrator levels. The results from two repeated tests show that (1) Metformin mass signal exhibited nonlinearity when isotopic Metformin-d6 was used as IS at lower concentrations, or nonisotopic Omeprazole was used as IS at all eight different concentrations. The standard curves between the Metformin response against its concentration with various concentration of IS are shown in Figure S1-A,B (Supporting Information); (2) In the case of different concentrations of isotopic Enalapril-d5 or nonisotopic Omeprazole as the IS, Enalapril exhibited good linearity within the calibration range. The standard curves between the Enalapril response against its concentration at various concentration of IS are shown in Figure S1-C,D (Supporting Information). Furthermore, with Metformin at a very low concentration (10.0 ng/mL), its response became significantly suppressed by a high Metformind6 concentration. The deterioration of LLOQ was proportional to the IS concentration. In other words, the use of high SIL-IS concentration would reduce the sensitivity for Metformin analysis (Figure 1A and Table 1). In Group 2, when a nonisotopic compound was used as internal standard, there was no cross interference between the Metformin and the IS at eight different concentration levels (Figure 1B and Table 1). Enalapril in Groups 3 and 4 exhibited good linearity, the mass

50.0, 100.0, 200.0, 500.0, 1000.0, and 2000.0 ng/mL were added in the calibration series, respectively. Each calibration series was prepared in duplicate. Quality control (QC) samples were prepared at the concentrations of 30.0 ng/mL (low quality control, LQC), 200.0 ng/mL (middle quality control, MQC), and 1600.0 ng/mL (high quality control, HQC) in methanol, and each QC level was prepared in five replicates. All solutions were vortexed for 30 s and then centrifuged (4 °C, 12000 rpm) for 5 min. The supernatant was transferred into sample vials for injection. The injection volume for all LCMS/MS analyses in this work was 10 μL. Statistical Analysis. Calibration curves of general method were fitted with weighted (1/X or 1/X2) or nonweighted linear regression. The calculation was performed and processed by equipped Xcalibur software. The raw data of CE method was also acquired by Xcalibur software and processed by a built program with Microsoft Excel and GraphPad Prism 5 (GraphPad Software Inc., San Diego, CA). The accuracies of methods were expressed by the mean relative error (RE%) of the back-calculated concentrations to nominal concentrations of three concentration levels of QC. The criteria of accuracy was set at within ±15% for QCs in accordance to the U.S. FDA guidance for bioanalytical method validation.

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RESULTS AND DISCUSSION Nonlinearity Problem. According to some previous studies, the responsive behavior of an analyte was found to be changing with the change of SIL-IS concentration.8,10 There are two types of IS for LC-MS/MS quantifications: nonisotopic internal standards (NIS-IS) and stable isotope labeled internal standard (SIL-IS). In the present study, we analyzed four groups of analytes with different IS at different concentrations to investigate the issue. Group 1 consisted of C

DOI: 10.1021/acs.analchem.9b00947 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry Table 1. Response Variation of IS at Eight Different Concentrations within the Standard Curve Range of 10.02000.0 ng/mLa Metformin Metformind6 Concn of IS (ng/ mL) 10 20 50 100 200 500 1000 2000

Enalapril

Omeprazole

Enalaprild5

Omeprazole

RSD (%) of IS response within standard curve range 47.5 43.2 38.7 33.0 24.0 15.2 9.7 7.6

6.0 5.8 4.5 5.1 4.6 8.3 5.1 4.6

12.8 3.2 4.0 3.7 9.1 3.8 5.8 4.8

9.0 14.5 7.7 3.3 3.1 3.0 4.1 3.2

Figure 2. Simulation relationship between the analyte and its SIL-IS. When the MS behavior was nonlinear, the sensitivity (represented by the slope, r) of analyte decreased with the concentration increase. The analyte and its SIL-IS were treated as one substance in the course of ionization. The addition of SIL-IS (C is ) would make the concentration of analyte (Ca) become Ct (Ct = Ca + Cis), suppressing the sensitivity of analyte from r1 to r2, leading the response variation of analyte with the concentration of SIL-IS increase and vice versa.

a

Metformin and Enalapril were analytes, Metformin-d6 and Enalaprild5 were their SIL-ISs, respectively, and Omeprazole was their common nonisotopic internal standard. The relative standard deviation (RSD%) was calculated based on the response of IS at a fixed concentration within the standard curve range. Each calibration series was prepared in duplicate.

experiment results also clearly validated this conjecture that no such interference was observed for linear systems (Groups 3 and 4) and nonisotopic internal standard cases (Groups 2 and 4). Therefore, it is the nonlinearity that causes the signal interference between an analyte and its SIL-IS. New Calibration Method. Conventionally, quantitative analysis with LC-MS/MS is based on the calibration between the analyte concentration and the signal ratio of the analyte to IS. A study found that there were different degrees of ionization suppression between the analyte and its SIL-IS.4 A SIL-IS is made by replacing some atoms in its corresponding analyte with heavier isotopes, such as 1H by 2H, 12C by 13C, 14 N by 15N, and 16O by 18O.9 Researchers discovered the replacement of the carbon bound hydrogen with deuterium would slightly alter the lipophilicity of the molecule29 and change its ionization efficiency. In fact, stock solutions for standard and SIL-IS often are not prepared at the same time, and sometimes different storage time result in some difference in signal strength between the analyte and its SIL-IS. Accidental errors may also occur in solution preparation. For these reasons, we introduced a correction factor γ to compensate the difference in ionization efficiency between the analyte and its SIL-IS. The factor γ can be established by injecting the same amount of analyte and SIL-IS, then taking the ratio of their signals, as shown in eq 1 below:

signal of Enalapril was independent of the IS concentration, and the IS mass signal was independent of Enalapril concentration (Figure 1C,D and Table 1). The results from the groups demonstrated that there were interferences between the analyte and its SIL-IS when the calibration curve was nonlinear. For a nonlinear system, the response of SIL-IS at a given concentration would decrease with the increase in analyte concentration, and reversely, an increase in the SIL-IS concentration would suppress the analyte response. This was a unique problem in using stable isotope labeled substance as internal standard in this study. Furthermore, the use of a SIL-IS would always worsen the LLOQ, and the higher the SIL-IS concentration, the worse the LLOQ. When the calibration curve was linear, the inference problem was not obvious. Explanation for the Nonlinearity Problem. Since an analyte and its SIL-IS have exactly the same structure but differ only in their molecular weight (i.e., their masses), the interference can happen only if the analyte and its SIL-IS both have the same ionization efficiency and detection sensitivity in the mass spectrometer. In other words, a mass spectrometer responds to an analyte and its SIL-IS in the same way other than mass separation. The addition of a SIL-IS into the analyte solution would be equivalent to increasing the analyte concentration. When the analyte response in the mass spectrometer is not linear, an increase in analyte concentration would move the signal response upward along the parabolic response curve. The further upper it moves on the parabolic curve, the lower its tangential slope becomes and the lower the response sensitivity is. The simulation relationship between the analyte and its SIL-IS was shown in Figure 2. Therefore, for a nonlinear system, signal responses of the analyte and its SIL-IS always decrease when the concentration of either the SIL-IS or analyte is increased. Suppose the analyte concentration is Ca, the concentration of SIL-IS is Cis, and total concentration becomes Ct (= Ca + Cis), the signal decrease caused by nonlinearity is proportional to the concentration difference ΔC (= Ct − Ca). Therefore, signal suppression or interference occurs in a nonlinear system and when SIL-IS is used. Our

γ = R a /R is

(1)

where Ra and Ris are the responses of the analyte and its SIL-IS, respectively. For a nonlinear system, we can start with a linear equation as the first order of approximation that would lead to the following eq 2: R a /Ca = γR is/Cis

(2)

where Ca and Cis represent the concentration of analyte and SIL-IS, respectively. Applying the isometric theorem, we would arrive at the following relationships: R a + γR is R γR is ∝ a = Ca + Cis Ca Cis (3) D

DOI: 10.1021/acs.analchem.9b00947 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

Table 2. Comparison Results of the Accuracy between CE Calibration and the Conventional Calibrations for Metformin with Different Concentrations of SIL-ISa concn of SIL-IS (ng/mL) γ value

calibration method

QC level (ng/mL)

10

20

50

100

200

500

1000

2000

30 200 1600 30 200 1600 30 200 1600 30 200 1600

−0.7 −32.3 −83.5 63.3 6.9 9.1 5.3 10.4 23.7 5.4 11.5 25.2

3.3 9.7 19.7 55.4 0.1 8.6 5.0 8.3 29.3 3.1 11.3 33.9

8.5 12.1 5.7 62.2 5.1 10.5 6.1 9.3 26.2 6.6 13.8 32.2

−0.8 4.8 −1.2 67.2 −0.6 0.4 −1.9 5.6 20.8 −2.5 7.3 23.1

15.0 7.5 14.8 59.9 6.1 7.9 14.9 11.6 22.4 20.6 14.2 25.1

14.4 4.4 5.7 32.5 7.1 5.8 12.3 8.7 10.9 8.0 3.4 5.4

15.3 8.6 6.7 62.7 8.3 0.4 7.0 8.4 9.1 7.0 8.4 9.1

27.4 13.2 14.2 29.2 10.7 9.3 17.4 31.8 35.8 −4.1 5.7 8.7

CE

none

1.01

general method with different weighting factor

1/X

1/X2

The acceptable accuracy was set as within ±15% for QC.

a

by quadratic regression. Three levels of the quality control samples were set at concentrations of 30.0 ng/mL (LQC), 200.0 ng/mL (MQC), and 1600.0 ng/mL (HQC). The SIL-IS at eight different concentrations were used to prepare eight calibration series. The value of γ was calculated by averaging the selected value of Ra/Ris from eight calibration series, where Ca and Cis were equal. Eventually, γ could be determined by injecting the same amount of analyte and its SIL-IS at the same concentration. The concentration of each QC sample was back-calculated from standard curves with different SIL-IS concentrations by CE fitting and by the common linear fitting with 1/X weighting, 1/X2 weighting, and without weighting, respectively. Table 2 comparatively showed the accuracy of analytical results from different calibration approaches. The data in Table 2 demonstrated that, in a nonlinear situation, the CE method would yield acceptable accuracy (the mean relative error were within ±15% for QCs) when the SIL-IS level was about in the middle of the calibration range. The accuracy of the MQC and the HQC with low SIL-IS concentration (10.0− 20.0 ng/mL), and the LQC with high SIL-IS concentration (1000.0−2000.0 ng/mL) were out of range. The possible reason for the unsatisfactory accuracy is that the fraction Ca/ (Ca + Cis) draws closer to 0 or 1 when Cis becomes very high or very low. In the former case, the Ca would be swamped in the uncertainty of Cis, while in the latter, Cis would contribute as noise to increase the uncertainty of Ca. Therefore, in both cases, the accuracy of Ca deteriorates. Evidently, for the CE method, the SIL-IS concentration should be set close to the middle of the calibration range. As the results show in Table 2, the accuracy for the conventional method with no weighting is consistently unsatisfactory for the low QC level, and weighting using 1/X or 1/X2 improves getting satisfactory data with the higher concentration of IS. However, unlike the CE method, there is not as clear a trend for when accuracy degrades. Example 2: CE Calibration for Linear Response Compared with General Method. Experiments were carried out for Enalapril at calibration concentrations range of 10.0, 20.0, 50.0, 100.0, 200.0, 500.0, 1000.0, and 2000.0 ng/mL, within which the analyte responses were linear and can be well fitted by linear regression. This was to examine the accuracy of CE method on substance with linear behavior. Three levels of the quality control (QC) samples were set at concentrations of 30.0 (LQC), 200.0 (MQC), and 1600.0 ng/mL (HQC). Eight calibration series were prepared as well with each at a different

Rearranging eq 3 would result in Ra Ca ∝ R a + γR is Ca + Cis

(4)

Equation 4 is the second order of linear proximation between Ra and Ca since it took the interference from the SILIS into consideration. For easy reference, we named eq 4 as a component equation (CE). Calibrating LC-MS/MS data with CE not only corrects nonlinear responses but also compensates the interference between the signal responses of the analyte and its SIL-IS. We established the correlation equation between Ra/(Ra + γRis) and Ca/(Ca + Cis) as standard curve of CE at first and then back-calculated the concentration of samples. Comparative Study of Component Equation Method and the Conventional Quantitative Method. As we expected, the standard curves resulted from CE calibration had perfect linearity with the correlation coefficient greater than 0.99. The standard curves of Metformin and Enalapril adjusted by CE method are shown in Figures S2 and S3 (Supporting Information). In order to contrast the LC-MS/MS quantitative accuracy between CE calibration and other commonly used calibrations, we took Metformin and Enalapril for nonlinear and linear examples. The samples we analyzed were prepared in methanol, therefore, the LC-MS/MS methods involved in this study were validated based on fit-for-purpose approach to check sensitivity, precision, accuracy, stability of autosampler, and validity of stock solutions. All methods were conformed to the U.S. FDA guidance for bioanalytical method validation. The validation data is shown in Tables S1 and S2 (Supporting Information). For the comparative study between CE method and the conventional quantitative method, we have conducted three groups of parallel comparative experiments for each of the following drugs. In this manuscript, only a representative group of experimental data was presented, the other data are shown in Tables S3 and S4 (Supporting Information). Example 1: CE Calibration for Nonlinear Response Compared with Conventional Calibrations. Experiments were carried out by a validated method for Metformin quantification at calibration concentrations of 10.0, 20.0, 50.0, 100.0, 200.0, 500.0, 1000.0, and 2000.0 ng/mL. In the absence of IS, the response of Metformin was nonlinear within the calibration concentration range, which could be well fitted E

DOI: 10.1021/acs.analchem.9b00947 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry

Table 3. Comparison Results of the Accuracy between CE Calibration and the Conventional Calibrations for Enalapril with Different Concentrations of SIL-ISa concn of SIL-IS (ng/mL) γ value

calibration method

QC level (ng/mL)

10

20

50

100

200

500

1000

2000

30 200 1600 30 200 1600 30 200 1600 30 200 1600

9.5 14.1 58.2 61.8 7.5 12.7 8.9 8.8 22.5 9.7 12.5 28.6

9.5 11.2 −5.2 75.4 6.7 7.4 6.7 8.6 22.0 7.0 10.7 24.7

7.2 11.5 13.4 12.6 6.4 9.9 7.2 12.3 14.1 7.5 13.8 19.8

4.7 1.8 0.9 31.4 −3.3 −2.6 4.9 5.9 13.3 4.7 4.5 11.5

10.2 7.2 13.5 39.8 5.5 7.7 5.3 14.5 24.5 7.5 18.2 28.8

7.3 1.9 9.0 6.3 7.2 10.0 0.2 6.3 9.9 −2.3 5.9 9.9

12.9 0.7 10.3 −8.9 1.3 8.9 −2.3 2.3 9.1 −3.4 2.1 9.0

20.2 7.2 −0.7 51.2 14.9 3.9 −23.0 5.7 2.5 −28.8 5.2 2.4

CE

none

0.66

general method with different weighting factor

1/X

1/X2

The acceptable accuracy was set as within ±15% for QC.

a

SIL-IS concentration. The eight SIL-IS concentrations were corresponding to the eight analyte calibration levels. The comparison of accuracy between the conventional calibrations and the CE calibration for Enalapril was shown in Table 3. The accuracies obtained from CE calibration were acceptable with the SIL-IS concentration from 20.0 ng/mL to 1000.0 ng/mL, the unsatisfactory results were obtained at HQC with the SIL-IS concentration at 10.0 ng/mL and the LQC with the SIL-IS concentration at 2000.0 ng/mL (the acceptable accuracy results were set within ±15%). Similar to the CE calibration for Metformin, very high or very low concentration of Cis would lead to more deviation, resulting in unsatisfactory results. For the conventional method, the satisfactory results were obtained irregularly at various concentrations of IS. With no weighting factor, the satisfactory results were obtained with the IS concentration of 50.0, 500.0, and 1000.0 ng/mL. With 1/X weighting factor, the results were acceptable when the concentration of IS were 50.0, 100.0, 500.0, and 1000.0 ng/mL. Weighting with 1/X 2, the satisfactory results were obtained with the IS concentration of 100.0, 500.0, and 1000.0 ng/mL. By comparison, the CE method showed superior accuracy over the conventional calibration methods. This example also demonstrated that the CE calibration was not only suitable for the nonlinear situation, but applicable to linear cases as well.

SIL-IS. It does not require any subjective weighting factors or quadratic fitting for nonlinear LC-MS/MS data regression. With various concentrations of SIL-IS, results calculated from CE calibration showed comparable or better than that from conventional linear regression. This study also found that the best SIL-IS concentration should be set close to the middle of the calibration range. The CE method may provide a reliable way for LC-MS/MS quantification both for nonlinear and linear systems.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.9b00947. Additional information as noted in the test, including the standard curves of analyte response against its concentration with various concentrations of SIL-IS, the standard curves of analyte adjusted by CE method with various concentrations of SIL-IS, and the general validation data (PDF)

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AUTHOR INFORMATION

Corresponding Authors

CONCLUSION This study was aimed at the nonlinearity problem in LC-MS/ MS quantification using stable isotope-labeled analyte as internal standard. Nonlinearity not only cause the calibration curve to be parabolic, but also induce signal cross suppression between the analyte and its SIL-IS. Through this study, we found that a mass spectrometer responds to an analyte and its SIL-IS indifferently, other than mass separation. Experiments with four analyte-IS pairs demonstrated that an addition of the SIL-IS into a sample would be equivalent to an increase in the concentration of the analyte. Such a concentration increase would practically change (mostly decrease) the sensitivity of the analyte when the analyte responsive behavior is nonlinear. Based on this result, we proposed to use the component equation (CE) as a calibration function. The CE calibration was proved capable of offering good linearity and effective correction on signal suppression between the analyte and its

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Guoping Zhong: 0000-0002-5753-4578 Author Contributions ∥

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

The authors would like to acknowledgement the financial supports provided by the National Key Research and Development Program [No. 2017YFC0909303]; Guangdong Province Key Laboratory of Construction Foundation [No. 2017B030314030]. F

DOI: 10.1021/acs.analchem.9b00947 Anal. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.analchem.9b00947 Anal. Chem. XXXX, XXX, XXX−XXX