CTC hydrochloride (CAS No. 64-72-2) was obtained from Sigma-Aldrich (St. Louis, MO, USA). All chemicals used were of analytical and HPLC grades, and ultrapure water was used in the analysis. The 0.5 mM CTC solution was prepared in methanol and stored at −20°C. The sensitivity was monitored by calculating the peak area according to changes in the operational conditions of the HPLC-MS/MS. CTC analysis was performed using an Agilent 1200 HPLC system (Agilent, Palo Alto, CA, USA) equipped with a reversed phase column (Agilent ZORBAX Eclipse Plus C18, 2.1 × 100 mm I.D., 1.8 μm) (Fig. 1). The mobile phase was composed of 40% A (acetonitrile) and 60% B (0.1% formic acid in water). Addition of formic acid into the mobile phase enhances the sensitivity due to the sufficient amount of proton to promote the desolvation of CTC [29]. The flow rate was 0.2 mL/min with an injection volume of 15 μL. The column temperature was maintained at 25°C using a thermostatically controlled column oven in the HPLC system.

The 6410 Triple Quad Mass Spectrometer (Agilent, Palo Alto, CA, USA) and electrospray ionization (ESI) source in a positive mode interface was operated in multiple reaction monitoring (MRM) mode (Table 1). The CTC transition 479 (M + H⁺) to 462 m/z was monitored for a dwell time of 200 ms. The fragmentor voltage and collision energy were maintained at 100 V and 15 eV, respectively. The mass spectrometer interface in positive mode was operated under conditions of 4,000 V capillary voltage, 300°C drying gas temperature, 7 L/min drying gas, and 40 psi nebulizer pressure.

The RSA was used to determine the relationship between peak area at 462 m/z and operational conditions of the HPLC-MS/MS. Sensitivity tests were conducted by changing one factor and fixing the other variables, i.e., OFAT analysis, using the conditions described in Table 1. Then, three factors were selected as independent variables for RSA among the seven operational factors: solvent composition, injection volume, nebulizer pressure, drying gas flow rate, drying gas temperature, fragmentor voltage, and collision energy. The experimental conditions for the RSA were identified based on the central composite in cube design (CCD) using a 3 × 2 orthogonal design [30–31]. The conditions of the center point were fixed as close as possible to the best conditions from the OFAT analysis. The center point was replicated five times to calculate the experimental error. This type of design was used to minimize the number of trials needed to obtain statistically relevant results.

A sequential procedure was conducted as follows: collecting data from the given conditions for the RSA, estimating polynomials (Eq. (1)), and checking the adequacy of the model. For the statistical analysis, Design Expert software (version 6.0.6, Stat-Ease, Minneapolis, MN, USA) was used. The least squares method was used to estimate the parameters in approximating polynomials.

where

The peak area of the product ion of CTC, 462 m/z, was tested for the seven factors (Fig. S1). First, solvent composition and injection volume were tested as control factors for the HPLC compartment. The peak area significantly depends on the composition of the acetonitrile in the mobile phase (Fig. S1(a)). The range between 60% and 80% of acetonitrile was optimum. The mechanism for the solvent composition influence on sensitivity is unclear, but a high concentration of acetonitrile in the mobile phase was expected to increase the ionization efficiency by increasing the evaporation capacity of the mobile phase. In Fig. S1(b), the peak area was stable at 2.32 ± 0.40 × 10⁶ disregarding the injection volume in the range of 2–15 μL. Therefore, only acetonitrile concentration was selected for RSA.

Second, the three ionization chamber control factors, i.e., nebulizer pressure, drying gas flow rate, and drying gas temperature, were tested (Figs. S1(c) to S1(e)). The nebulizer pressure regulates the efficiency of the liquid sample spray on the tip of the needle. After spraying, the high temperature and the rapid flow of the drying gas evaporate the water and solvent contents to enhance the ionization of CTC. Among the three factors, only the drying gas flow rate was considered as a major factor for RSA because a dramatic increase in the peak area was observed at a drying gas flow rate of 10 L/min. The drying gas temperature is an important factor to produce desolvated CTC ion, but the temperature range of 250–350°C showed saturated effect on the sensitivity. A previous study also showed that wide range of drying gas temperature, 150–300°C, exhibited the limited effect on the sensitivity of mass spectrometry [32].

Third, the fragmentor voltage and collision energy of the mass spectrometry compartment were tested. These factors are related to the ionization and dissociation of the precursor molecule of 479 m/z. In the sensitivity test shown in Fig. S1(f) for fragmentor voltage, the range between 100 and 150 V was optimum. Generally, a moderate fragmentor voltage in the MRM mode intensifies the ionization of the precursor molecule. However, in this study, a high fragmentor voltage divided the precursor molecule into smaller precursor molecules, including 444 and 462 m/z, rather than of 479 m/z (data not shown). In this case, the peak intensity for 462 m/z obtained in the final detection device was reduced because the first quadrupole only allowed 479 m/z to the next step of the collision induced dissociation (CID) to produce 462 m/z in the MRM mode.

For the best CID, the collision energy should be optimized to generate the 462 m/z product ion by splitting the 479 m/z molecule. An excessively high collision energy splits the 479 m/z molecule into product ions smaller than 462 m/z in the MRM mode, such as 444 and 154 m/z. Using the test presented in Fig. S1(g), 15 eV was identified as the optimum collision energy value for the higher peak area.

The important control factors, including solvent composition, drying gas flow rate, fragmentor voltage, and collision energy, showed significant effects on peak area. Among these factors, the drying gas flow rate was not selected as an independent variable for RSA because the experimental conditions could be optimized by simply increasing the drying gas flow rate. However, the independent variables that showed curvatures in the peak area in the experimental range, such as the solvent composition, fragmentor voltage, and collision energy, were selected as major factors for RSA; varying their values could create different optimum conditions for the HPLC-MS/MS.

The list of experimental conditions and corresponding peak areas for RSA are described in Table 2. At the center point, 100 V, 15 eV, and 60% for fragmentor voltage, collision energy, and solvent composition, respectively, were obtained from Section 3.1 as presumed optimum conditions. The drying gas flow rate was increased to 10 L/min, and the other factors remained the same, as in Table 1. The testing ranges for the largest peak area of 462 m/z were chosen as 71.7–128.3 V, 7.9–22.1 eV, and 45.9–74.1% for fragmentor voltage, collision energy, and solvent composition, respectively. An additional trial was undertaken to verify the accuracy of the model prediction by randomly selecting experimental conditions (Trial 16 in Table 2) after obtaining the best model equation that fit the experimental data. The average value of the peak area at the center point was 8.11 ± 0.29 × 10⁶ and the standard deviation was 3.55%.

Initially, a regression with 15 trials, including the center point (Trials 1 to 9 in Table 2), was conducted using a first-order model with least squares to investigate the location of the optimum condition. The step sizes of the variation from the center point were 20 V, 5 eV, and 10% for fragmentor voltage, collision energy, and solvent composition, respectively. The p value for the lack of fit was significant and the regression coefficient for the peak area was not significant at a 5% α-level. Therefore, an additional six trials (Trials 10 to 15 in Table 2) were utilized to find a more appropriate equation to regress the experimental responses at various conditions with a second or higher order model. The step sizes of the variation were expanded to 28.3 V, 7.1 eV, and 14.1% for fragmentor voltage, collision energy, and solvent composition, respectively.

A high R² value indicates a good explanative power, which is calculated from the ratio of the regression sum of squares to the total sum of squares. In contrast, the adjusted R² value explains any bias in the R² value by taking into account the degree of freedom of the independent variables. The R² and adjusted R² values for the basic quadratic model (Eq. (2)) were 0.9835 and 0.9650, respectively. The equation was modified to obtain a better quality model, represented by the increased R² and adjusted R² values.

where

The addition of the (fragmentor voltage × collision energy²) and (collision energy × solvent composition²) terms to Eq. (2) increased the R² and adjusted R² values to 0.9884 and 0.9673, respectively (Eq. (3)). The p value of the regression was significant at a 0.1% α-level and the lack of fit was not significant at a 5% α-level. These results indicated that the partial cubic model was an accurate representation of the data. The residual plots represent the difference between the experimental and calculated values for the model (Fig. S2), and showed no patterns or trends. Therefore, the model described in Eq. (3) was an adequate approximation for the peak area variance according to the variation in fragmentor voltage, collision energy, and solvent composition (Fig. 2).

To find the optimum condition for the largest peak area in the experimental ranges, the response surface of Eq. (3) was analyzed by setting the partial derivatives of the equation to zero with respect to the independent variables. The optimum conditions for the highest response were identified as 114.9 V, 15.7 eV, and 70.9% for fragmentor voltage, collision energy, and solvent composition, respectively, which are near the conditions for Trial 10 in Table 2 (128.3 V, 15 eV, and 60% for fragmentation voltage, collision energy and solvent composition, respectively) where the largest peak area, 8.45 × 10⁶, was observed. The peak area under optimum conditions was estimated as 8.73 × 10⁶. In a separate experiment to verify using triplicate analysis of the expected optimum conditions, the 9.18 ± 0.80 × 10⁶ result showed an insignificant difference from an estimated value of 8.73 × 10⁶, i.e., 5.2%. The predictability of the model obtained in this study was also validated using the randomly selected conditions for Trial 16 in Table 2. There was only a 0.56% error between the predicted value from the model, 6.62 × 10⁶, and observed value, 6.58 × 10⁶. These validations under the optimum and random conditions showed the high accuracy of the model in predicting the response surfaces of the peak area for the target product ion when changing the fragmentor voltage, collision energy, and solvent composition.

A statistical analysis of the independent variables in the model shows that the (solvent composition) and (collision energy²) terms were significant for the peak area at a 0.1% α-level; and (fragmentor) and (solvent composition²) terms were significant for the peak area at a 5% α-level. However, the (fragmentor voltage × collision energy), (fragmentor voltage × solvent composition), (collision energy × solvent composition), (fragmentor voltage × collision energy²), and (collision energy × solvent composition²) two-way interactions were not statistically significant.

In addition to the statistical significance, the coefficient for each term affects the variation in the peak area. To compare the relative effects of terms on peak area, Eq. (3) was converted to Eq. (4), which reflects the normalized step sizes instead of actual values. The normalized step size from the center point is described in Table 2. The largest contribution was attributed to (collision energy²) due to the largest absolute value of the coefficient, 1,857,422. In the same manner, the contributions from terms in Eq. (4) were evaluated. It was considered that interactions had the least influence on the peak area, with rankings of 6 to 10 among the eleven terms. In sum, the interaction between fragmentation voltage, collision energy, and solvent composition had no statistical significance and contribution to variation in the peak area. However, the interaction terms could improve the R² value, i.e., the predictability of the model.

The sensitivities of individual factors were tested at the optimum conditions. One factor was varied at a time while the other independent variables were fixed. Fig. S3 shows the most significant effect of collision energy among the three independent variables. The significant effect of collision was also expected in Eq. (4), with the largest absolute value of coefficient for (collision energy²). However, the peak area responded with less sensitively to fragmentor voltage and changes in solvent composition.