3.2. Method Optimization
Traditionally analytical methods were developed and optimized by using an “one factor at time” (OFAT) approach. In OFAT optimizations each factor is varied within an appropriate range while the other factors are kept constant; the drawback of this approach being that it does not allow evaluation of the interaction between the studied factors [20
Design of experiments (DoE) approaches have been implemented more and more frequently in the development of analytical methods in the last 20 years; this strategy can produce more reliable results using fewer experiments than in OFAT based on a set of statistical tools [21
An OFAT strategy was applied for screening purposes to identify the influence of analytical parameters on the analytical responses (chiral resolution, migration times of the two enantiomers) and to identify significant parameters followed by a face centered composite design (FCCD) for optimization.
In the OFAT screening the influence of five analytical parameters (BGE concentration, CD concentration, applied voltage, system temperature, injection pressure) on three analytical responses (chiral resolution, migration times of the enantiomers) was studied. The results obtained in the OFAT screening are presented in Table 1
Migration times increased as the BGE concentration (25–100 mM) increased with no noticeable impact upon chiral resolution.
Migration times increased with an increase in CD concentration (5–15 mM) but the relationship between CD concentration and chiral resolution was not linear, as resolution increased when increasing CD concentration from 5 to 10 and decreased when increasing CD concentration from 10 to 15. CD concentration has an optimum value, as the difference in the apparent electrophoretic mobility between the two enantiomers will reach a plateau at a certain CD concentration and will decrease at higher CD levels.
With the increase of applied voltage (20–30 kV) the migration times decreased with a small decrease in chiral resolution as well.
Migration time and chiral resolution decreased with the increase of system temperature (15–25 °C), due to the BGE lower viscosity.
Injection parameters influenced the shape and amplitude of the peaks and consequently chiral resolution but had an insignificant effect upon migration times.
Based on the results obtained in the OFAT screening three analytical factors were selected for further optimization using a FCCD: CD concentration (factor A), system temperature (factor B), and applied voltage (factor C). Two analytical responses were registered: chiral resolution (response 1) and migration time of the second migrating enantiomer (response 2).
FCCD is an optimization design in which the star points are at the middle of each factorial space face (α = ± 1), requiring three levels for each factor [20
We conducted a total of 15 experiments where the selected parameters were varied on three levels (−1, 0, +1) with five center point injections: CD concentration (8, 10, 12 mM), system temperature (15, 17.5, 20 °C), and voltage applied (20, 25, 30 kV). The other parameters, considered to be less significant based on the initial OFAT screening results, were kept constant in the optimization experiments: buffer concentration 25 mM, buffer pH 2.5, injection 50 mbar/s.
The experimental design plan and the response factors are presented in Table 2
A statistical analysis was performed, in order to include or exclude the linear terms (A, B, C), interaction terms (AB, AC, BC), and the quadratic terms (A2
) using the variance of analysis model (ANOVA). Based on ANOVA, the following regression models were obtained:
R = +1.39 + 0.030* A − 0.19* B − 0.14* A * C − 0.50* A2 + 0.068* B2 − 0.052* C2
Analysis time (min) = +5.84 + 2.41* A − 0.61* C + 1.25* A2 − 0.47* C2
The regression models were evaluated based on the determination of the coefficients R2 and R2 -adj; values of 0.9958 and 0.9927 for R and 0.9790 and 0.9707 for analysis time, respectively, were obtained. Pred R2 values of 0.9902 for R and 0.9330 for analysis time were in a reasonable agreement with Adj R2 values. The values indicate that our models are suitable for navigation in the design space.
3-D response surface plots for the two analytical responses are presented in Figure 2
The error provided by regression model lack-of-fit is significantly smaller than random pure error, indicating that the regression models are fitted.
Derringer’s desirability functions were used to maximize and optimize the two analytical responses. The statistical software numerical optimization function was used for setting targets for each analytical response to produce optimal conditions: short migration times and high chiral resolution. Numerical optimization feature will search the design, using the models created in the analysis, generating a list of potential factor settings that provide responses that meet the defined criteria.
The optimum solution generated by the software was the following: 10 mM CM-β-CD concentration, system temperature 15 °C, applied voltage 25 kV. Applying the optimum analytical conditions, we succeeded in the chiral separation of VFX enantiomers in about 6 min with a resolution of 1.64.
A typical electropherogram obtained using the optimized conditions is presented in Figure 3
Analytical parameters of the optimized method are presented in Table 3
The migration order of the enantiomers could not be established by spiking since we did not have pure enantiomers at our disposal.
3.3. Analytical Performance
The analytical performance of the method was evaluated in terms of intra-day and inter-day precision, accuracy, linearity, and limit of detection (LOD) and quantification (LOQ) were calculated.
Intra-day precision was measured by injecting an 0.5 mg/mL racemic VFX standard, six times on the same day; while inter-day precision was checked by injecting an 0.5 mg/mL racemic VFX standard, six times a day for three consecutive days. The precision for migration times and peak area was evaluated through RSD (%) values.
To determine reliability of the method, recovery tests were performed using standard addition method. An appropriate amount of VFX capsule powder was weighed and spiked with a specified amount of the standard and each sample was analyzed in triplicates. The good recovery values are an indication of high accuracy.
A calibration curve was constructed by plotting peak area versus concentration of the analyte; eight different concentrations (0.1–2 mg/mL) were used and measurements were performed in triplicate. Correlation coefficients of over 0.99 indicates a good linearity of the method.
LOD and LOQ were calculated as the standard deviation of regression equation divided with the slope of the regression equation multiplied by 3.3 and 10, respectively.
The results obtained during the verification of analytical performance are summarized in Table 4
The developed method was applied for the determination of VFX enantiomers in pharmaceutical formulation containing 75 mg R,S
-VFX racemate. Good agreement between the developed method and the values claimed by the manufacturer was obtained, with an enantiomer ratio of approximately 1:1 (Table 5
3.4. Molecular Modelling of VFX-CD Complexes
Molecular modelling methods are useful tools to obtain information on the interaction energy as well as preliminary data of the geometry of the inclusion complexes.
The starting geometries of VFX enantiomers and the CM-β-CD structures based on CSD data are presented in Figure 4
In the case of CD-analyte complexes, the chiral recognition mechanism is generally based on inclusion complexation where the analyte fits in the CD cavity, so VFX enantiomers were docked in the cavity of the CD, trying to simplify calculations. Two specific inclusion orientations of the guest molecule in the complex were considered, where VFX is inserted at either the wider or the narrower cavity of the CD. To characterize molecular properties of inclusion complexes more accurately, its structure was further optimized using a quantum semiempirical method (RM1).
To improve the accuracy of the theoretical calculations, finding the low-lying energy conformation is mandatory. The energy of the complexation is defined as the energy difference between the optimized complex and the isolated host and guest energies, on their complex conformations.
Computational calculations for the inclusion complexes of the two enantiomers with CM-β-CD showed that differences in the stability of these complexes generates chiral stereoselectivity. Through theoretical calculations we can predict the migration order of the enantiomers, based on the establishment of the more stable the inclusion complex. Due to the difference in energy between S-VFX and R-VFX (13.12 kcal/mol) complexes with CM-β-CD, it was established that the inclusion of S-VFX is energetically more favorable by 13.12 kcal/mol (−66.47 kcal/mol for S-VFX by comparison with −53.35 kcal/mol for R-VFX). This indicates that S-VFX fits more closely into the cavity of the CD and this selective interaction allows chiral discrimination. Taking into consideration these results, we can conclude that the migration order is R-CIT followed by S-CIT.
Structures of the optimized CM-β-CD inclusion complex with S
-CIT and R
-CIT are shown in Figure 5