486 COMPUTER-ASSISTED METHOD DEVELOPMENT Table 10.1 Computer-Simulation Options Option Comment 1. Simulation of chromatograms for isocratic %B or different gradient conditions, and temperature Section 10.1 2. Use of resolution maps for easy selection of optimized conditions Section 10.1 3. Selection of best column conditions Section 10.1 4. Isocratic predictions from gradient data Simulation of changes in t G and T also allow predictions of isocratic elution as a function of %B and T (Sections 10.2.1, 10.2.3.1). 5. Designated-peak selection R s and R s -maps calculated only for peaks of interest; peaks not overlapping the peak of interest are ignored (Section 10.2.3.2). 6. Change in other conditions Separation can be simulated for any variables that affect selectivity (Table 2.2); a change in column requires experimental data for that column (Section 10.2.3.3) 7. Computer-selection of a multi-segment gradient Manual or automated searches possible (Section 10.2.3.4) 8. Peak tailing Can be simulated (Section 10.2.3.5) 9. Two-run procedures for improving resolution Different gradients for different peaks in same sample (Section 10.2.3.6) noted that although isocratic separation can be predicted from gradient experiments, the prediction of gradient elution from isocratic experiments is not convenient; for maximum flexibility starting method development with gradient experiments often makes the most sense. 10.2.3.2 Designated-Peak Selection Many chromatograms contain peaks that are of no direct interest to the chromatog- rapher. For example, the analysis of biological or environmental samples for specific compounds may be complicated by the presence of numerous interfering peaks. Similarly, in preparative separation (Chapter 15), we are often concerned with the purification and recovery of a single compound in the sample. When only some peaks in the chromatogram are of interest, it is important to resolve each of these peaks from all remaining peaks—but not the separation of interfering peaks from each other, as this is unnecessary. As an illustration of designated-peak selection, consider the example of Figure 10.4, but assume that it is required to assay only peaks 3, 8, and 10 in the presence of the remaining ‘‘interfering’’ peaks. A final separation is therefore required that will separate these three peaks from each other and from any other peaks that might overlap 3, 8, and 10 (this is a much easier task than the separation of all 11 peaks from each other). 10.2 COMPUTER-SIMULATION SOFTWARE 487 Time (min) 4.9 4.3 3.7 3.1 2.5 1.9 1.2 0.6 0.0 R s °C 50 40 30 gradient time t G (min) 20 40 60 80 100 (a) (b) 3 0246810 10 8 5-100% B in 22 min 49°C; R s = 4.9 (peaks 3, 8, 10 only) Figure 10.6 Optimizing the separation of selected peaks in the ‘irregular’ sample of Figure 10.4; use of computer simulation to select optimum values of gradient time and tem- perature for the separation of peaks 3, 8, and 10 from remaining peaks. (a) Resolution map; (b) best separation for 5–100% B in 33 minutes and 49 ◦ C. Using computer simulation, we can designate peaks 3, 8, and 10 as peaks of interest. When a resolution map for designated peaks only is next requested (peaks 3, 8, and 10 in this example), values of the critical resolution R s will be plotted versus temperature and gradient time for just peaks 3, 8, and 10. This is illustrated in Figure 10.6a, which indicates conditions for the best separation (cross-hairs and arrow in a). The corresponding chromatogram is shown in Figure 10.6b (numbers mark peaks of interest). As anticipated, the possible critical resolution for the separation of only three of the 11 peaks in this sample is much greater (R s = 4.9) than for the separation of all 11 peaks (R s = 2.1 in Fig. 10.4); a shorter run time is also required (11 vs.14 min). The latter ‘‘excess’’ resolution can be traded for a much shorter run time by a suitable change in column conditions. For example, reducing column length by half and doubling the flow rate reduces run time to 3 minutes, while maintaining a resolution of R s = 3.0 and leaving column pressure unchanged. 10.2.3.3 Change in Other Conditions Other conditions that affect selectivity can be modeled by computer simulation by varying either one or two different conditions at a time. In addition to the 488 COMPUTER-ASSISTED METHOD DEVELOPMENT choices of Figure 10.2, any combination of %B or gradient time, temperature, B-solvent mixtures, mobile phase pH, buffer, or ion-pair reagent concentration can be simulated for RPC. Normal-phase and ion-exchange separations can also be modeled for most conditions that affect their selectivity. 10.2.3.4 Computer Selection of the Best Multi-Segment Gradient Other than for cleaning the column as in Figure 9.11b, two-segment gradients are used primarily for one of three general purposes. First, the resolution of bunched peaks at the beginning of the gradient often can be improved with an isocratic hold (e.g., Fig. 9.9c, d). Second, the separation of critical peak-pairs at the beginning and end of a separation—when the peak-pairs respond differently to changes in gradient steepness—can be improved by the use of segments of differing steepness (e.g., Figs. 9.12a,b). Third, runs with excessive resolution at the end often can be shortened by using a steeper gradient to compress the end of the chromatogram (e.g., Fig. 10.5). Computer simulation can provide a trial-and-error examination of a large number of two-segment gradients (as in Fig. 10.5), followed by the selection of a gradient that yields the best selectivity for maximum resolution and/or shortest run time. However, the application of this approach to several samples [15] suggests that the advantage of two-segment gradients for further improvement in resolution (as in the example of Fig. 9.12b) is often marginal; thus it is rare for a segmented gradient to improve resolution by as much as 0.5 units. Segmented gradients for the purpose of maximizing resolution can be developed automatically by some computer software [15–18]. When compared with the simultaneous optimization of gradient time and separation temperature (a preferred approach), there appears to be little advantage in the sole use of multi-segment gradients for increasing resolution [15]. A minor exception is the use of segmented gradients for the separation of samples that contain large molecules such as proteins (Section 9.2.2.5). A disadvantage of segmented gradients is that they can contribute to problems in method transfer because of gradient rounding (Section 3.10.1.2; [19]). 10.2.3.5 Peak Tailing Peak tailing should be corrected before experimental method-development separa- tions are carried out. For some samples, however, this may not be possible. Because separation can be strongly affected by peak tailing, computer simulation should take this into account. Some examples of peak tailing were shown in Figures 2.16 and 2.17, all of which were created by computer simulation with the DryLab program. While moderate peak tailing usually has a limited effect on separation and resolution, this is not the case for two compounds whose size is very different (compare Fig. 2.16e and Fig. 2.16d). In these cases it is important that computer simulation can reliably simulate peak tailing, based on the tailing of peaks in the input runs. 10.2.3.6 Two-Run Procedures for the Improvement of Sample Resolution When the sample contains 15 or more components, it may be difficult to achieve adequate resolution (e.g., R s ≥ 2; see Section 2.3.4) in a single gradient separation. An alternative, occasionally successful, approach for such samples is the use of two 10.2 COMPUTER-SIMULATION SOFTWARE 489 different gradient procedures (or ‘‘runs’’) for the same sample [20], but with no change in either the column or the A- and B-solvents. For example, the two runs might each use a different gradient time t G and a different temperature T that allows the two runs to be carried out without any additional operator intervention during the analysis of a set of samples. All samples would be assayed first with one set of conditions, followed by their re-analysis using the second set of conditions (different values of t G and T). The goal is adequate resolution of every peak of interest in one or the other of the two runs, which then allows an assay of all the peaks in the sample based on a composite of the two runs. By means of computer simulation, it is relatively easy to select best conditions for each of the two runs so that overall critical resolution for the sample is maximized [20]. A similar approach has been described for isocratic separation, which uses two ‘complementary’ runs [21]. 10.2.3.7 Examples of Computer Simulation as Part of Method Development Numerous examples of computer simulation have been reported, as summarized in [22] and p. 119 of [2]. Many of these reports are intended as illustrations of computer simulation, or as examples of its accuracy. Other publications report the use of computer simulation for the actual development of a routine method. Fifteen examples of the latter, more representative applications of computer simulation are summarized in Table 10.2. 10.2.4 Peak Tracking When varying conditions during method development that can change relative retention, it is important to keep track of which peak is which in each chromatogram. Means for matching peaks were discussed in Section 2.7.4. Peak tracking is even more important for computer simulation because errors in peak assignment often result in large errors in predicted separations. Automated peak tracking, based on relative retention and peak areas, is included in DryLab software. Because this software’s procedure is restricted to relatively simple separations (≤10 peaks, limited changes in relative retention, no more than 10-fold variation in peak area), its accuracy can be improved by the use of supplemental software (Peak Match ® ; Molnar Institut, Berlin). Mass spectrometric detection may be required for samples containing many peaks whose sizes vary over orders of magnitude. Once peak tracking has been carried out for the experiments used in computer simulation, peaks are automatically matched for all subsequent simulations. Despite the importance of accurate peak tracking when using computer simulation, errors in peak tracking will be apparent when predicted and experimental separations are compared (the predicted retention times for one or more peaks will not match the corresponding experiment). 10.2.5 Sources of Computer-Simulation Software Computer simulation software is available from several companies or groups, for example, ACD/LC Simulator ® (Advanced Chemistry Development, Toronto, Ontario, Canada); ChromSmart ® (Agilent, Palo Alto); ChromSword ® (Merck KGaA, Darmstadt, Germany); DryLab ® (Molnar Institut, Berlin), Turbo Method Development (PerkinElmer, Shelton, CT); Osiris R [31]; and Preopt-W R [32]. These software packages are for the most part limited to simulations of RPC. 490 COMPUTER-ASSISTED METHOD DEVELOPMENT Table 10.2 Examples of Computer Simulation as Part of Method Development for ‘‘Real’’ Applications Feature Results (Comments) Designated peak selection; optimization of gradient time [8] a. Measurement of a single impurity in a sample that contained >15 components b. Preparative purification of a single peak c. Measurement of three components in samples containing as many as 10 related compounds Best multi-segment gradient [8] Analysis of a 7-component sample Best multi-segment gradient [23] Multi-segment gradients were able (for the first time) to separate all 19 of the 30S ribosomal proteins; 33 of 34 of the 50S ribosomal protein could be similarly separated. Best multi-segment gradient [8, 18, 24] Separations of 7-, 12-, and 19-component mixtures by means of segmented gradients Vary T and t G plus a change in B-solvent[8, 25] Where the use of an initial B-solvent was unsuccessful, variation of T and t G was repeated with different B-solvents (ACN, MeOH, or 2-propanol) Isocratic predictions from gradient data [8] Computer simulation for varying T and t G provided excess isocratic resolution, followed by changes in column length and flow rate for reduced run time Selection of best column and gradient time [26] 16 columns were investigated for the best separation of a 6- and an 8-component mixture Selection of best column and B-solvent [27] Two gradient runs (t G = 20and50min)were repeated for three columns and two B-solvents (ACN,MeOH);separationwiththebest column/solvent choice was further optimized using a Plankett-Burmann design Selection of best column, temperature and gradient time [28] Gradient time and temperature were optimized for 9 different columns; this allowed the best conditions to be selected for various separation goals Variation of gradient time and ratio of ACN and MeOH in B-solvent [29] B-solvent was varied from 0–100% ACN/MeOH (4 solvent mixtures), each of which was run at two gradient times for the optimum separation of a 8-component mixture Simple variation of gradient time or isocratic % [30] Four examples for different samples In addition Virtual Column (Dionex, Sunnyvale, CA) is available for predicting separations by ion chromatography. See also several reviews and/or comparisons of software of this kind [9–11, 33]. For a detailed review of some technical requirements of computer simulation, see [34]. (New products are introduced with regularity as others are discontinued, so this list is by no means complete and is expected to soon be out of date.) 10.3 OTHER METHOD-DEVELOPMENT SOFTWARE 491 10.3 OTHER METHOD-DEVELOPMENT SOFTWARE Besides the software for computer simulation as described above, other software packages are available to support method development. Some features of such software include the following: • predictions of solute retention from molecular structure • predictions of solute pK a -values from molecular structure • selection of reversed-phase columns with similar or different selectivity • expert systems for method development Sections 10.3.1 to 10.3.5 briefly review software for these applications but do not exhaust the possibilities for computer-assisted method development. 10.3.1 Solute Retention and Molecular Structure Attempts at relating chromatographic retention to solute molecular structure have a long history. In principle, if it were possible to predict solute retention as a function of molecular structure and experimental conditions (mobile phase, stationary phase, temperature), there would be no need for actual experiments during method development. As discussed in Section 2.6.7, the possibility of reliable predictions of this kind appears remote at present. Nevertheless, predictive software based on molecular structure has been offered at various times in the past—and will probably continue to be offered in the future. ChromSword and the ACD/LC Simulator (cited in Section 10.2.5) provide an alternative option for computer simulation, where one or more experimental runs are replaced by predictions of retention based on molecular structure. An independent evaluation of this feature [11] concluded that ‘‘Predictions based on molecular structure alone are not very accurate and are not likely to provide useful separation information.’’ Similar software has been available for more specialized applications (protein digests [35], metabolized drugs [36]), but the reliability of such software is similarly in question. More recent attempts at predicting RPC separation are somewhat more promising [37] but aim at a different goal—namely peak identification when used in combination with mass spectrometric detection. The required predictive accuracy for the latter goal is much less than would be required for optimizing resolution. 10.3.2 Solute pK a Values and Molecular Structure Compound pK a values determine solute retention as a function of mobile-phase pH. Consequently a knowledge of pK a values for compounds present in the sample can be useful for planning and interpreting method-development experiments (Section 7.2). Software for the retrieval or estimation of pK a values (water as mobile phase and 25 ◦ C) can be obtained from various sources (Advanced Chemistry Development, Toronto, Ontario, Canada; Intertek ASG Laboratory, Manchester, UK). However, as noted in Section 7.2.3, values of pK a vary with both temperature and mobile-phase composition. The latter values of pK a may be of limited use in practice, where organic-water mobile phases are the rule and temperature can vary. Experiments where mobile-phase pH is varied will generally provide more reliable estimates 492 COMPUTER-ASSISTED METHOD DEVELOPMENT of sample pK a values for method development (see Section 7.2 and the examples of Fig. 7.3). The approximate pK a values summarized in Table 7.2 for different functional groups or compound classes should suffice in most cases for method development. 10.3.3 Reversed-Phase Column Selectivity RPC column selectivity can be characterized by values for five column characteris- tics (Section 5.4.1). Appropriate software (Column Match ® , Molnar Institut, Berlin; http://www.usp.org/USPNF/columnsDB.html) allows different columns to be com- pared in terms of selectivity, in turn allowing the selection of replacement columns of similar selectivity, or columns of very different selectivity when changes in relative retention are needed (Section 5.4). 10.3.4 Expert Systems for Method Development The possibility of fully automatic method development by means of computer software (expert systems) has been under investigation since the mid-1980s [9, 38]. Ideally information on the nature of the sample and separation goals would be entered into the computer, the computer would recommend initial separation conditions, a sample would be injected, the results of this first injection would be interpreted by the computer, and subsequent experiments would be selected by the computer and used for successive computer simulations—until a successful separation is obtained. Any problems encountered during this process would be solved by the computer. Previous attempts in this direction either have failed to achieve commercial success or have been limited to optimizing separation after the user selects initial conditions [39]. However, the appeal of this approach is strong, so improved products are sure to be introduced in the future. 10.4 COMPUTER SIMULATION AND METHOD DEVELOPMENT Computer simulation is not intended to replace the various strategies for method development that have been presented in preceding chapters. Rather, computer simulation should be used to augment real trial-and-error experiments during method development. The selection of conditions for adequate resolution in a minimum separation time is often the main consideration in method development—a goal for which computer simulation can be especially effective. Two examples of the use of computer simulation in this way are presented in Sections 10.4.1 and 10.4.2. 10.4.1 Example 1: Separation of a Pharmaceutical Mixture Consider the development of an RPC method for a sample that consists of 12 derivatives of lysergic acid diethylamide (LSD). An initial gradient separation with the conditions recommended in Table 9.3 was first carried out (Fig. 10.7a). From this initial chromatogram with a 10-minute gradient, it appears that gradient elution is the preferred option (Section 9.3.1, t R /t G = 0.33), although isocratic elution is also possible. Therefore the next step is to carry out a separation with a 30-minute 10.4 COMPUTER SIMULATION AND METHOD DEVELOPMENT 493 1.0 0.5 020 02040 40 60 80 100 R s Gradient time t G (min) Time (min) Time (min) 5-100% B in 10 min 35°C R s = 0.6 5-100% B in 30 min 35°C R s = 0.6 5-20% B in 50 min; 35°C 300-mm column; 0.7 mL/min R s = 1.7 1 024 2 3 7 8 9 10 11 12 1 2 3 7 8 9 10 0246 11 + 12 4 6 5 4 6 5 Time (min) (a) (b) (c) (d) Figure 10.7 Illustration of a strategy for method development based on the use of computer simulation for the selection of final separation conditions. Sample: mixture of 12 derivatives of lysergic acid diethylamide (LSD). Conditions: C 18 column; acetonitrile/water gradients; other conditions varied. (a) 5–100% B in 10 minutes, 100 × 4.6-mm (3-μm) C 18 column; 35 ◦ C; 2.0 mL/min; (b), same as in (a), except 5–100% B in 30 minutes; (c) resolution map; (d) final separation with conditions indicated in figure. Simulated separations based on data of [13]. gradient (other conditions the same); this separation is shown in Figure 10.7b. Resolution (R s = 0.6) is unacceptable for either run, but computer simulation can be used to determine a gradient time for maximum resolution. The resolution map of Figure 10.7c indicates two ‘‘optimum’’ gradient times: 19 minutes (R s = 0.9), and 80 minutes (R s = 1.1). The average value of k ∗ = 6fort G = 19 min is preferable to k ∗ = 25 for t G = 80 min; a shorter gradient time is also generally preferred. 494 COMPUTER-ASSISTED METHOD DEVELOPMENT Because resolution is still far from adequate, the best next step is to explore a further change in selectivity. Our recommendation is to carry out two additional experimental separations where temperature is varied, which with the two sep- arations of Figure 10.7a,b yield the experimental design shown in Figure 10.2b (gradient times of 10 and 30 min, temperatures of 35 and 55 ◦ C). Unfortunately, resolution was not improved by this simultaneous optimization of gradient time and temperature. Because resolution is unacceptable (R s = 0.9) at this stage of method develop- ment, conditions for improved resolution need to be explored—by further changes in either selectivity or column conditions. A change in selectivity can proceed by selecting a different B-solvent (e.g., methanol instead of acetonitrile), column (Section 5.4.3), or mobile-phase pH (for samples that contain acids or bases). When computer simulation is used, changes in column conditions and the gradient do not require additional experiments, so this option should be pursued first. The simplest change in column conditions is an increase in column length, accompanied by decrease in flow rate, so as to maintain column pressure the same. For the present sample, a 300-mm column with a flow rate of 0.7 mL/min gives a resolution of R s = 1.7, but with an increase in gradient time to 171 minutes. We can next reduce the gradient range to save time. Figure 10.7d shows the resulting separation for a gradient of 5–20% B in 50 minutes, where R s = 1.7. Other changes in gradient shape were explored in an effort to improve the compromise between resolution and separation time, but these proved unsuccessful. Considering the difficulty of the separation, the observed resolution might be considered adequate. However, if the 50-minute run time is a problem (because of a large number of samples to be assayed), further attempts at optimizing selectivity should be explored—as suggested above. Any increase in resolution as a result of improved selectivity can always be traded for a shorter run time (Sections 6.4.2, 9.3.6). While the example of Figure 10.7 might be regarded as somewhat disappointing in its outcome, the amount of experimental effort required for an exploration of all these options was minimal (four experimental runs)—as was the time required for all these simulations. At the same time a number of unsuccessful options have been dispensed with, allowing the chromatographer to focus on other, more promising lines of attack. 10.4.2 Example 2: Alternative Method Development Strategy The preceding example emphasizes the optimization of gradient time and/or tem- perature for the optimization of selectivity. Other, similar strategies are illustrated in Figure 10.2. A different approach is to change one condition at a time (e.g., column type), while optimizing either %B or gradient time for each set of condi- tions. An example of this approach is described in [27], for the separation of a 10-component pharmaceutical mixture that contained three active ingredients and seven impurities or degradation products. All solutes were non-ionizable, so buffer- ing the mobile phase was not required. This sample required gradient elution, and the method-development approach followed is outlined in Figure 10.8a. The initial experiments evaluated three different columns for the separation: NovaPak C18, Luna C18, and Discovery RP Amide C16. Gradients from 10 to 90% B were carried out in times of 20 and 50 minutes, using either acetonitrile 10.4 COMPUTER SIMULATION AND METHOD DEVELOPMENT 495 Method Development Approach [27] 0 0 5 10 15 5101520 20 (min) (min) simulated actual computer simulation Select 3 different columns NovaPak C18 Luna C18 Discovery RP Amide C16 Vary B-solvent 25% MeOH/ACN 50% MeOH/ACN 75% MeOH/ACN 10–90% B in 20 and 50 min B = MeOH or ACN (4 experiments each column) Most promising column Discovery RP Amide C16 Best choice of B-solvent (50% MeOH/ACN) and gradient (45–68%B in 23 min) (a) (b) (c) Figure 10.8 Separation of a pharmaceutical mixture of 10 components using computer sim- ulation. (a) Outline of experiments; (b) simulated final separation (DryLab); (c) actual final separation. Conditions for both (b)and(c): 250 × 4.6-mm Discovery RP Amide C16 column; 45–68% B in 23 minutes (B is 50% MeOH/ACN); 40 ◦ C; 1.0 mL/min. Adapted from [27]. (ACN) or methanol (MeOH) as B-solvent (12 initial scouting runs). Each of the six pairs of experiments for a given column and B-solvent was used as input for computer simulation (DryLab), in order to establish the optimum gradient time. The most promising results were obtained for the Discovery RP Amide C16 column with ACN as B-solvent, but one pair of compounds were still overlapped (R s ≈ 0). However, comparing results for the two B-solvents with the Discovery RP Amide C16 column suggested that a mixture of ACN and MeOH as B-solvent would enable the separation of all 10 compounds in the sample. Mixtures of 25, 50, and 75% MeOH/ACN as B-solvent were tried. These resulted in an adequate separation for the sample with 50% MeOH/ACN as the B-solvent. Finally, the gradient range was optimized (45–68% B in 23 min) to give the predicted separation of Figure 10.8b, with the actual separation shown in Figure 10.8c. A similar method-development approach is described in [40], where 12 dif- ferent columns were evaluated with changes in temperature and mobile phase, using computer simulation to interpret results and guide further experiments. How- ever, such a large number of method-development experiments will rarely be . companies or groups, for example, ACD/LC Simulator ® (Advanced Chemistry Development, Toronto, Ontario, Canada); ChromSmart ® (Agilent, Palo Alto); ChromSword ® (Merck KGaA, Darmstadt, Germany);. Molecular Structure Attempts at relating chromatographic retention to solute molecular structure have a long history. In principle, if it were possible to predict solute retention as a function of. Berlin), Turbo Method Development (PerkinElmer, Shelton, CT); Osiris R [31]; and Preopt-W R [32]. These software packages are for the most part limited to simulations of RPC. 490 COMPUTER-ASSISTED METHOD