Anal. Chem. 2008, 80, 268-278
Comparison of the Practical Resolving Power of One- and Two-Dimensional High-Performance Liquid Chromatography Analysis of Metabolomic Samples Dwight R. Stoll, Xiaoli Wang,† and Peter W. Carr*
Department of Chemistry, University of Minnesota, Smith and Kolthoff Halls, 207 Pleasant Street SE, Minneapolis, Minnesota 55455
Two-dimensional liquid chromatography (2DLC) has become a mainstay of proteomics research due to its higher peak capacity compared to one-dimensional LC (1DLC). Because of the long analysis times typically associated with 2DLC (tens of hours) and its use primarily in proteomics applications, 2DLC in the context of general HPLC has been regarded as a niche technique for use in analysis of mixtures containing hundreds to thousands of components compared to the far more common techniques of isocratic and gradient elution 1DLC. A significant next step in the analytical development of 2DLC is to consider using its higher resolving power to reduce the analysis time of rather “simple” mixtures, in the range of only tens to hundreds of chemical constituents. The chief objective of this paper is to provide guidance to practitioners who need to decide whether 1DLC or 2DLC gives the superior separation in a given analysis time. Conditional peak capacities are predicted for fully optimized 1DLC and practical 2DLC separations of the low molecular weight constituents of an extract of corn seed at several analysis times using a model based on the chromatographic properties of compounds that are representative of real mixtures of lower molecular weight species. Two important corrections to the ideal 2DLC peak capacity are made to account for both incomplete usage of the separation space and the serious effect of first-dimension undersampling; this allows, we believe for the first time, a fair comparison of the resolving power of 1D- and 2DLC under realistic conditions. The predicted optimum conditions are then used to carry out experimental separations of low molecular weight corn seed extract, and peaks are counted in each 1D- and 2DLC chromatogram. Based on comparisons of both the predicted peak capacities and number of peaks observed in experimental chromatograms, we believe that practical 2DLC will be superior to fully optimized gradient 1DLC for separations lasting more than only about 10 min. This crossover time is much shorter than intuitively expected, and we believe this finding will inevitably have a major 268 Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
impact on the practice of 2DLC in liquid-phase separations in general. There has been a tremendous increase in interest in twodimensional liquid chromatography (2DLC) in the past decade. This has been greatly influenced by the complexity of biological samples in the fields of proteomics1 and metabolomics.2 As Schure3 recently pointed out, three decades ago, Karger, Snyder, and Horvath4 and later both Giddings5 and Guiochon6 described the potential of multidimensional separations, namely, the potential for huge improvements in resolving power over one-dimensional counterparts. Realizing that the resolving power of one-dimensional HPLC (1DLC) is seriously limited, many proteomics researchers have adopted two-dimensional HPLC-mass spectrometry as their standard analytical tool.1 Since the pioneering work of Erni and Frei7 and then Bushey and Jorgenson8 in comprehensive online two-dimensional HPLC, the foremost barrier to the wide application of the technique has been its low speed, typically on the order of several hours per chromatogram.9 Several reports have appeared showing complete comprehensive, online 2DLC separations on 30-60-min time scales. Clearly the cycle time of the second-dimension separation is perhaps the most important factor in establishing the overall time to achieve the desired two-dimensional peak capacity, but other issues are involved. Surely the rate of peak capacity production in the second dimension is also important, as is the conditional peak capacity of the first-dimension separation. Several groups have used * To whom correspondence should be addressed. E-mail: petecarr@ chem.umn.edu. † Present address: 1800 Concord Pike, Wilmington, DE 19850. (1) Issaq, H. J.; Chan, K. C.; Janini, G. M.; Conrads, T. P.; Veenstra, T. D. J. Chromatogr., B 2005, 817, 35-47. (2) Dunn, W. B.; Ellis, D. I. Trends Anal. Chem. 2005, 24, 285-294. (3) Schure, M. R. In Multidimensional Liquid Chromatography: Theory, Instrumentation and Applications; Cohen, S. A., Schure, M. R., Eds.; Wiley & Sons: New York, 2008. (4) Karger, B. L.; Snyder, L. R.; Horvath, C. An Introduction to Separation Science; Wiley & Sons: New York, 1973. (5) Giddings, J. C. Anal. Chem. 1984, 56, 1258A-1260A, 1262A, 1264A. (6) Guiochon, G.; Beaver, L. A.; Gonnord, M. F.; Siouffi, A. M.; Zakaria, M. J. Chromatogr. 1983, 255, 415-437. (7) Erni, F.; Frei, R. W. J. Chromatogr. 1978, 149, 561-569. (8) Bushey, M. M.; Jorgenson, J. W. Anal. Chem. 1990, 62, 161-167. (9) Stoll, D. R.; Li, X.; Wang, X.; Porter, S. E. G.; Rutan, S. C.; Carr, P. W. J. Chromatogr., A 2007, 1168, 3-43. 10.1021/ac701676b CCC: $40.75
© 2008 American Chemical Society Published on Web 12/06/2007
multiple second-dimension columns operated in parallel to improve the throughput of the second dimension.10-12 Tanaka and coworkers,13 and others14-16 have used monolithic columns to improve the throughput of the second dimension. Our approach has been to use high-temperature HPLC conditions (>100 °C) as suggested by Horvath17 and modest instrument modifications to allow ultrafast gradient elution in only ∼20 s, while maintaining a high peak capacity (∼1 peak/s). This approach has been applied to the separations of tryptic peptides18 and low molecular weight constituents in a plant leaf tissue extract (i.e., a metabolomics application).19 Several recent reviews of the field give an overview of recent progress and applications of the 2DLC technique.1,9,20-23 Although there have been many reports on the performance of 2DLC, we are only aware of one systematic comparison of the performance of conventional 1DLC, and 2DLC, which was concerned with peptide separations and involved rather long (5240 min) second-dimension analysis times.24 Recent work by ourselves19 and others25,26 has shown that optimal 2DLC separations must involve very fast (subminute time scale) seconddimension separations, when the effect of broadening of firstdimension peaks by undersampling is considered. In comprehensive online 2DLC, fractions of the effluent from the first-dimension column are sequentially injected into a second-dimension column. The low speed of the second-dimension separation (typically 20 s to several minutes per second-dimension run) results in an overly coarse sampling of the first-dimension peaks as they elute from the first-dimension column. Murphy et al.27 and Seeley28 studied the broadening of individual first-dimension peaks as a function of the first-dimension sampling rate. Later Horie et al.25 applied the findings of Seeley to correct estimates of 2D peak capacity as part of a theoretical study of optimization in 2DLC. Most recently,29 we established a means of correcting 2D peak capacity estimates to account for first-dimension undersampling that is based on averages over the entire comprehensive 2DLC separation process (10) Venkatramani, C. J.; Patel, A. J. Sep. Sci. 2006, 29, 510-518. (11) Wagner, K.; Miliotis, T.; Marko-Varga, G.; Bischoff, R.; Unger, K. K. Anal. Chem. 2002, 74, 809-820. (12) Wagner, K.; Racaityte, K.; Unger, K. K.; Miliotis, T.; Edholm, L. E.; Bischoff, R.; Marko-Varga, G. J. Chromatogr., A 2000, 893, 293-305. (13) Ikegami, T.; Hara, T.; Kimura, H.; Kobayashi, H.; Hosoya, K.; Cabrera, K.; Tanaka, N. J. Chromatogr., A 2006, 1106, 112-117. (14) Dugo, P.; Skerikova, V.; Kumm, T.; Trozzi, A.; Jandera, P.; Mondello, L. Anal. Chem. 2006, 78, 7743-7750. (15) Venkatramani, C. J.; Zelechonok, Y. Anal. Chem. 2003, 75, 3484-3494. (16) Zhang, J.; Tao, D. Y.; Duan, J. C.; Liang, Z.; Zhang, W. B.; Zhang, L. H.; Huo, Y. S.; Zhang, Y. K. Anal. Bioanal. Chem. 2006, 386, 586-593. (17) Antia, F., D.; Horvath, C. J. Chromatogr. 1988, 435, 1-15. (18) Stoll, D. R.; Carr, P. W. J. Am. Chem. Soc. 2005, 127, 5034-5035. (19) Stoll, D. R.; Cohen, J. D.; Carr, P. W. J. Chromatogr., A 2006, 1122, 123137. (20) Dugo, P.; Cacciola, F.; Kumm, T.; Dugo, G.; Mondello, L. J. Chromatogr. A 2007, In Press, Doi: 10.1016/J.Chroma.2007.06.074. (21) Dixon, S. P.; Pitfield, I. D.; Perrett, D. Biomed. Chromatogr. 2006, 20, 508529. (22) Shalliker, R. A.; Gray, M. J. Adv. Chromatogr. 2006, 44, 177-236. (23) Shellie, R. A.; Haddad, P. R. Anal. Bioanal. Chem. 2006, 386, 405-415. (24) Gilar, M.; Daly, A. E.; Kele, M.; Neue, U. D.; Gebler, J. C. J. Chromatogr., A 2004, 1061, 183-192. (25) Horie, K.; Kimura, H.; Ikegami, T.; Iwatsuka, A.; Saad, N.; Fiehn, O.; Tanaka, N. Anal. Chem. 2007, 79, 3764-3770. (26) Schoenmakers, P. J.; Vivo-Truyols, G.; Decrop, W. M. C. J. Chromatogr., A 2006, 1120, 282-290. (27) Murphy, R. E.; Schure, M. R.; Foley, J. P. Anal. Chem. 1998, 70, 15851594. (28) Seeley, J. V. J. Chromatogr., A 2002, 962, 21-27. (29) Davis, J. M.; Stoll, D., R.; Carr, P. W. Anal. Chem. 2007, in press.
rather than the behavior of just a single peak. Briefly, the fact that the first dimension is undersampled ultimately results in a loss of chromatographic resolution between a given pair of peaks in the 2DLC separation. In other words, when a 1D separation is sampled to carry out a 2D separation, some of the 1D peak capacity (which becomes the first dimension of the 2D system) is lost due to undersampling of first-dimension peaks,27,29 and this loss is traded for the peak capacity gain brought about by the peak capacity of the added second-dimension separation. It is the balance of these (and other9) losses and gains that determines whether converting a 1D separation to a 2D separation will be productive. These trade-offs are very much a function of the time scales of the two separations. Other authors have been rightfully critical of blindly using 2D separations and citing ideal peak capacities without due regard for these trade-offs;30,31 it is our opinion that this has become all too common in recent literature reports of 2DLC separations. In this work, we introduce a conceptual framework that is required for a full and fair comparison of the performance of 1Dand 2DLC separations at a given analysis time. For a given analysis time, which will be the better performing method, a 1D separation, or a 2D separation? Considering only the sampling broadening described above, it is obvious that in the limit of very short analysis times the 1D method must prevail, because in the 2D case only a few fractions of the first-dimension effluent will be taken during the analysis and most of the resolution gained in the first dimension will be lost. In the current work, the two methods are compared first using predictions of total peak capacity for each method, and then by counting the numbers of chromatographic peaks observed in experimental separations. Total peak capacities are predicted by extending a previously validated model, which allows accurate prediction of peak width and retention time under gradient elution reversed-phase HPLC conditions, using compounds that are representative of real samples rather than arbitrarily chosen retention window limits. In the 2D case, the concept of an effective first-dimension peak width is utilized, which accounts for the broadening of first-dimension peaks due to the undersampling effect. This correction is qualitatively similar to the correction suggested by Horie and co-workers.25 However, recent simulations of 2DLC separations using realistic numbers of components and sampling times29 have resulted in broadening factors (see below) that are quantatively different (i.e., ∼25% more broadening at one sample per 8σ peak width) from those calculated by Murphy et al. and Seeley and employed by Horie et al. Second, in real separations, only a fraction of the entire 2D separation space is occupied by peaks. This is accounted for by multiplying the ideal 2D peak capacity by the fraction of the 2D separation space that is occupied, a simple but effective method suggested by Gilar and co-workers.24 We emphasize the value in comparing 1D and 2D separations based on both predicted peak capacities and numbers of observed peaks as key metrics of performance. The virtue of using peak capacity as a metric of performance is that it can be predicted from theory based on established models of gradient elution (30) Blumberg, L. M. J. Chromatogr., A 2003, 985, 29-38. (31) Michels, D. A.; Hu, S.; Dambrowitz, K. A.; Eggertson, M. J.; Lauterbach, K.; Dovichi, N. J. Electrophoresis 2004, 25, 3098-3105.
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HPLC,32,33 augmented by the retention behavior of representative compounds that mimic the retention patterns of real samples. Although simple representations of 2D peak capacity (e.g., see eq 2) have been propagating for decades, the calculation of an effective (i.e., usable) 2D peak capacity that accounts for undersampling of first-dimension peaks29 and incomplete usage of the 2D separation space is far more complicated than the calculation of effective 1D peak capacities.34 Moreover, the calculations of Davis et al.35 have shown that 2D separations are inherently less effective at producing peaks than are 1D separations, on a per unit peak capacity basis. Obviously this difference in the effectiveness of 1D and 2D separations makes the comparison of 1D and 2D separations based on peak capacity alone very difficult at best and potentially very misleading. Herein lies the virtue of using the number of peaks observed in experimental separations as a key metric of performance; it is the most direct measure of the analytically useful resolving power of real separations. Of course, the down side to this metric is that it requires that the experimental separations be done, which is particularly costly in the 2D case where a huge number of interacting variables are subject to optimization.36 We have chosen to use a low molecular weight extract (i.e., no proteins and few peptides) of corn seed powder to compare the number of peaks observed in 1D and 2D separations at different analysis times. While these conditions do target a particular class of low molecular weight species, we believe the diversity of these molecules is such that the conclusions arrived at in this work can be justifiably applied to other separation problems involving mixtures of low molecular weight species. Finally, we note that no attempt has been made in this work to systematically study the effect of the conditions used in the second-dimension separation on the overall performance of the 2DLC system. A preliminary optimization was carried out previously,19 and we intend to address this factor in more detail elsewhere. The focus of the work described here is the development of a framework that allows a fair comparison of the performance of 1D- and 2DLC. In the 1D case, we have optimized separation conditions to maximize 1D peak capacity at different analysis times for one particle size (5 µm), temperature (40 °C), and pressure limit (400 bar). For the first-dimension separation in the 2D case, we have kept the particle size, temperature, and pressure limit the same as in the 1D case and optimized the remaining operational variables (i.e., column length (L) and final eluent composition (φf)) to maximize first-dimension peak capacity at different analysis times. The total 2D peak capacity is then calculated, taking into consideration the sampling broadening effect, incomplete usage of the 2D separation space, and the peak capacity of the second-dimension separation, which is calculated from measured, not predicted second-dimension peak widths. It is intuitively obvious that changing some parameters of the 1D
separation (i.e., increasing the temperature and pressure limit and decreasing the particle size) will improve the performance of the resulting 1D separation. To a crude approximation, these performance gains can also be realized in the 2D case by improving the performance of the first dimension of the 2D system in a similar manner.30 Thus, the primary contribution of this paper is to quantify the impact of adding the second-dimension separation to an existing 1D separation.
(32) Snyder, L. R.; Dolan, J. W. High-Performance Gradient Elution: The Practical Application of the Linear-Solvent-Strength Model; Wiley & Sons: Hoboken, 2007. (33) Wang, X.; Stoll, D. R.; Schellinger, A. P.; Carr, P. W. Anal. Chem. 2006, 78, 3406-3416. (34) Dolan, J. W.; Snyder, L. R.; Djordjevic, N. M.; Hill, D. W.; Waeghe, T. J. J. Chromatogr., A 1999, 857, 1-20. (35) Oros, F. J.; Davis, J. M. J. Chromatogr. 1992, 591, 1-18. (36) O’Hagan, S.; Dunn, W. B.; Knowles, J. D.; Broadhurst, D.; Williams, R.; Ashworth, J. J.; Cameron, M.; Kell, D. B. Anal. Chem. 2007, 79, 464-476.
(37) Wang, X.; Barber, W. E.; Carr, P. W. J. Chromatogr., A 2006, 1107, 139151. (38) Wang, X.; Stoll, D. R.; Carr, P. W.; Schoenmakers, P. J. J. Chromatogr., A. 2006, 1125, 177-181. (39) Dolan, J. W. LCGC North Am. 2005, 23, 130, 132, 134-135. (40) Koehne, A. P.; Dornberger, U.; Welsch, T. Chromatographia 1998, 48, 9-16. (41) Layne, J.; Farcas, T.; Rustamov, I.; Ahmed, F. J. Chromatogr., A 2001, 913, 233-242. (42) Sternberg, J. C. Adv. Chromatogr. 1966, 2, 205-270. (43) Atwood, J. G.; Golay, M. J. E. J. Chromatogr. 1981, 218, 97-122.
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THEORY Peak capacity is the most common metric of separation power in gradient elution HPLC. It is defined as the number of “wellresolved” (typically, but not necessarily taken as unit resolution) component zones that fit into a given separation window. Previously we showed that it is also acceptable to think of the real peak capacity as proportional to the average resolution of the peaks in the retention window. Thus, optimizing the peak capacity is the same as optimizing the average resolution.33 All of the 1D and 2D separations in this work use gradient elution reversedphase LC (RPLC) separations in each separation dimension. We previously developed and validated a model of gradient elution RPLC that allows optimization of peak capacity via accurate prediction of peak width and retention time for compounds of interest. The reader is referred to previous publications for a detailed description of the model and its application;33,37,38 here we present only information that is unique to this study which was used for subsequent prediction of 1D and 2D peak capacities. Prediction of Gradient Elution Retention Times. We followed the approach of Wang et al.33 to predict the retention times and peak widths of model compounds under gradient elution conditions at a given temperature. This approach uses the linear solvent strength theory of gradient elution.32 The dependence of column efficiency (N) on flow rate was accounted for using the van Deemter equation. The coefficients of the van Deemter equation (A, B, C) were determined from an experimental flow curve obtained for the Discovery HS-F5 column used in 1D and first-dimension separations in this work. The experimental reduced van Deemter coefficients were 2.4 ((0.1), 12.6 ((0.3), and 0.035 ((0.002), for the A, B, and C terms, respectively (nitrobutane, k′ ) 15). Although extracolumn contributions to the observed peak width are a legitimate cause for concern, we have deliberately neglected them in our predictions of 1D and 2D peak capacity. Contributions to the peak variance due to injection volume are negligible for most solutes because we are using gradient elution conditions in both dimensions and extensive analyte focusing occurs at the column inlet.39-41 Using well-established estimates of extracolumn broadening due to detector flow cell volume, a finite detector time constant,42 and dispersion in tubing connecting the column outlet to the detector cell,43 we estimated that the total
extracolumn contribution to the total peak variance was rarely more than a few percent, and never exceeded 10%. Further, these same estimates predicted that a large majority of this extracolumn contribution was due to dispersion of analytes in the connecting tubing. Our own experience (data not shown) has shown that even the best estimates of broadening due to dispersion in connecting tubing under the type of conditions employed in this work grossly overestimate the actual broadening that occurs in the tubing. Given the significant potential error associated with these estimates and their rather slight contribution to the total peak variance, we have elected to leave them out of our calculations altogether. Peak Capacity Optimization Strategy. In a previous report on the validation of the gradient elution model used here,33 we outlined a process to guide the analyst in optimizing operational variables to maximize peak capacity, and this process was generally followed in this work. Because the effects of variables such as flow rate and final eluent composition are very tightly coupled in gradient elution, the Solver function of Microsoft Excel was used for simultaneous optimization of flow rate (1DLC only), column length, and final eluent composition, with the following constraints. The maximum allowable system pressure was set to 350 bar. The initial mobile-phase composition in the 1DLC separation or first-dimension separation of 2DLC was fixed at 100% aqueous buffer. The maximum length of the column used in 1DLC separations or the first-dimension separation of 2DLC was set to 50 cm, and the inner diameter was fixed at 2.1 mm. In the 1D case, the flow rate was allowed to vary continuously from 0 to 5 mL/min, while in the 2D case, the first-dimension flow rate was fixed at 0.10 mL/min. The primary reason for the flow rate restriction in the first dimension of the 2D system is that the volume of first-dimension effluent injected into the second dimension is a function of the first-dimension flow rate and the sampling rate. Any attempt to optimize the first-dimension flow rate by increasing it would require a concomitant increase in the second-dimension injection volume or decrease in the sampling time. For the purposes of this study, we elected to fix the first-dimension flow rate, realizing that the optimum conditions for the first-dimension separation are not a global optimum as in the case of the 1DLC separations. In both cases, the final composition of the eluent in the 1D or first-dimension gradient was allowed to vary from 10 to 100% organic modifier (v/v). The search for “optimum” chromatographic conditions for 1D and 2D separations at different analysis times was based on the goal of maximizing the peak capacity of the separation (only the first dimension in the 2D case) for a given analysis time. Here analysis time is defined as the total time required for the gradient elution to develop, flush the system of strong (organic-rich) solvent after the gradient is finished, and re-equilibrate the HPLC column with one column volume of the initial solvent used in the gradient. Based on previous work,44 we calculated the time required to adequately flush the strong solvent from the system as two times the gradient delay time (tD) at a particular flow rate. Calculation of 1D and 2D Peak Capacities. The nuances of peak capacity calculations for 1D gradient elution separations (44) Schellinger, A. P.; Stoll, D. R.; Carr, P. W. J. Chromatogr., A 2005, 1064, 143-156.
were reviewed recently.33 The most realistic estimate of 1D peak capacity is given by eq 1
nc,1D )
(tR,last - tR,first) w
(1)
where tR,last and tR,first are the retention times of the last and first peaks observed in the separation space and w is the measured average 4σ peak width (assuming the peak width is independent of retention time). In experimental separations of the corn seed extract, we always observed peaks eluting at the column dead time, and therefore set tR,first equal to tm. Likewise, peaks were always observed near the end of the gradient separation, as the conditions were optimized such that the latest eluting metabolite of indole-3-acetic acid (indole-3-acetonitrile) would elute near the end of the gradient, and thus, we set tR,last equal to tm + tD + tg because it is possible for peaks to elute up to this time. The peak width in eq 1 was taken as the average peak width predicted for a mixture of seven low molecular weight compounds ranging in molecular mass from 181 to 376 Da (see Experimental Section). No significant correlation of peak width with retention time was observed under any conditions studied in this work. The calculation of 2D peak capacity is less straightforward and has been approached in a variety of ways by different investigators, causing substantial difficulty in comparing results from different o groups. The ideal 2D peak capacity (nc,2D ) for comprehensive 2D separations was stated by Karger et al. as4
noc,2D ) 1nc × 2nc
(2)
where 1nc and 2nc are the peak capacities of the first and second dimensions of the 2D system, respectively. For the purposes of the current study, we have calculated 2nc based on experimental separations using eq 1. The departure from ideality due to incomplete use of the 2D separation space has been discussed by a number of groups and reviewed recently.22,45 We believe the most pragmatic approach to dealing with this problem has been described by Gilar et al.,46 and we have adopted their approach here. Briefly, a grid is cast on the 2D separation space, dividing the space into a series of rectangular “time bins”. The fraction of bins that are occupied by observed chromatographic peaks is calculated and used to correct the ideal 2D peak capacity to account for incomplete use of the 2D separation space. We refer to this fraction of bins occupied as fcoverage. o must be made to A second significant correction to nc,2D account for the broadening of first-dimension peaks due to undersampling of the first-dimension separation. The impact of undersampling on the effective width of individual first-dimension peaks was studied by Murphy et al.27 and later by Seeley.28 Horie et al. then applied the findings of Seeley (based on behavior of individual peaks) to calculate a corrected 2D peak capacity, which accounts for undersampling of first-dimension peaks. Most recently,29 we have determined an empirical broadening factor that accounts for undersampling of first-dimension peaks, that is based (45) Cordero, C.; Rubiolo, P.; Sgorbini, B.; Galli, M.; Bicchi, C. J. Chromatogr., A 2006, 1132, 268-279. (46) Gilar, M.; Olivova, P.; Daly, A. E.; Gebler, J. C. Anal. Chem. 2005, 77, 64266434.
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on the effect of undersampling on ensembles of large numbers of overlapping peaks in simulated comprehensive 2D separations. Equation 3 is a simple approximation that allows the calculation of the expected first-dimension broadening factor (denoted as ), which is dependent only upon the ratio of the sampling time to the standard deviation (prior to sampling) of firstdimension peaks (ts/1σ); this expression was shown to be valid over the range 0.2 e ts/1σ e 16.
)
x
1 + 0.21
() ts
Table 1. Operational Parameters and Predicted Conditional Peak Capacities for 1D Separations tanalysis (min)
tg (min) L (cm)a F (mL/min) φib φfc tg + td (min) w1D (min)d nc,1De
2
(3)
1
σ
15
30
60
12 30 0.65 0 0.60 12.5 0.092 136
24 40 0.45 0 0.50 24.8 0.168 148
52 50 0.35 0 0.38 53.0 0.338 157
a Column length. b Initial eluent strength. c Final eluent strength. Average 4σ peak width based on predictions of seven low molecular weight standards e Conditional 1D peak capacity calculated using eq 1.
d
The brackets on β emphasize that this broadening factor is an average value determined by considering the effect of undersampling on all peaks observed in a 2D separation, rather than the behavior of a single, isolated first-dimension peak. can then be used to calculate an effective first-dimension peak width (1ws, as it appears in the 2D separation after sampling) as in eq 4 1
ws ) 1w
(4)
where 1w is the first-dimension peak width prior to sampling. In a previous report on the rate of peak capacity production in gradient elution HPLC, we introduced the concept of a conditional peak capacity.38 When 1D peak capacities are calculated using eq 1, it is obvious that changes in chromatographic conditions can have a significant impact on the value of the peak capacity, either by changing the fraction of the separation window that is occupied by peaks or by changing the average peak width (e.g., by changing the gradient time or flow rate). Since the magnitude o of the two corrections to nc,2D outlined above will also be heavily dependent on the conditions of the 2D separation, we refer to o the corrected value of nc,2D as a conditional 2D peak capacity, o′ nc,2D, which is calculated using eq 5. 1 2 no′ c,2D ) nc × nc × fcoverage ×
1
(5)
In using eq 5, 2nc was taken to be 28 and is based on experimental data rather than a prediction of second-dimension peak capacity. We arrive at the value of 28 using a second-dimension separation window of 17 s and an average second-dimension peak width (4σ) of 0.6 s (n ) 10, 0.58 ( 0.12 s), which is based on the observed widths of 10 randomly selected second-dimension peaks in one of the 2DLC separations of the corn seed extract (see below for second-dimension conditions). EXPERIMENTAL SECTION Reagents. Tyrosine, 5-hydroxy-L-tryptophan, tryptophan, riboflavin, indole-3-acetic acid, indole-3-propionic acid, and indole3-acetonitrile were purchased from Sigma-Aldrich (St. Louis, MO) at reagent grade or better and used without further purification. Acetonitrile was obtained from Burdick and Jackson (Muskegon, MI). Sodium dihydrogen phosphate was from JT Baker (Philipsburg, NJ), and sodium perchlorate was obtained from SigmaAldrich; sodium monohydrogen phosphate and perchloric acid (70%) were obtained from Fisher Scientific (Fairlawn, NJ). HPLC 272 Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
grade water was obtained in-house from a Barnstead Nanopure deionizing system (Dubuque, IA). This water was boiled to remove carbon dioxide and cooled to room temperature before use. All aqueous eluents were prepared gravimetrically ((0.01 g) and passed through a 0.45-µm nylon membrane filtration apparatus (Lida Manufacturing Inc., Kenosha, WI) immediately before use. None of the eluents used in this work were degassed prior to their use. Sample Preparation. A sample of low molecular weight standards used to assess the accuracy of peak capacity predictions and the precision of peak area and peak volume contained tyrosine, 5-hydroxy-L-tryptophan, tryptophan, riboflavin, indole-3acetic acid, indole-3-propionic acid, and indole-3-acetonitrile at concentrations of ∼20 µg/mL each dissolved in 20 mM sodium phosphate, 20 mM sodium perchlorate, pH 5.7. The corn seed used for 1D- and 2DLC separations was Silver Queen (Burpee, Warminster, PA) and was extracted as follows. Five grams of whole seed was ground to a fine, dry powder using a blender, followed by addition of 3.5 mL of acetonitrile and 1.5 mL of 20 mM sodium phosphate, 20 mM sodium perchlorate, pH 5.7. This mixture was sonicated in an ultrasonic bath (model PC3, L&R Manufacturing, Kearny, NJ) at room temperature for 3 h, followed by centrifugation to pellet the remaining insoluble material. The resulting supernatant was evaporated from 2 mL to ∼600 µL under vacuum at 50 °C using a rotary evaporator. The resulting sample was analyzed without further purification and stored at 38 °C until use. Instrumentation and Columns. 1DLC Separations. Conventional 1D separations were performed using a standard HP 1090 Series II liquid chromatograph controlled by version A.10.01 Chemstation software (Agilent Technologies; Wilmington, DE). This instrument was equipped with an autosampler, column thermostating compartment, and ternary DR5 pumping system. A state-of-the-art stand-alone photodiode array detector (Agilent Technologies model G1315C) was coupled to the HP 1090 LC system and controlled by B.01.03 Chemstation software. Reversedphase separations were carried out with a Discovery HS-F5 column (Supelco, Bellefonte, PA) using organic solvent gradients developed according to the programs in Table 1. The A solvent was an aqueous buffer composed of 20 mM sodium phosphate, and 20 mM sodium perchlorate at pH 5.7. An appropriate combination of mono- and dihydrogen sodium phosphate salts was used to
Table 2. Sequence of Events for 2DLC Instrument Components for Two Complete Second-Dimension Gradient Cycles time (s) 0 18 (21-a)a 21 25 40.2 (42-b)a 42
Figure 1. Schematic of instrumentation used for fast 2DLC.
prepare the pH 5.7 buffer without further pH adjustment. The B solvent was pure acetonitrile. A flow rate of 0.10 mL/min was obtained from a simple flow-splitting apparatus constructed using different lengths of fused-silica capillary tubing (50 µm i.d. × 360 µm o.d., Polymicro Technologies, Phoenix, AZ) and a low dead volume “tee” fitting. The total flow rate delivered by the HP 1090 pumping system was 1.0 mL/min, and thus, a split ratio of 10:1 was used to deliver a flow rate of 0.10 mL/min to the HPLC injector and column. The column outlet was connected directly to the photodiode array detector using a 1.0-m length of 50-µmi.d. fused-silica tubing. The effective gradient delay volume of this system, including all tubing required to connect the column and accounting for flow splitting, was determined to be 0.04 mL, using the conventional technique.47 2DLC Separations. The basic features of the 2DLC system used in this work were adapted from the design of Bushey and Jorgenson8 and were described in detail in a previous publication.18 The first dimension of the 2DLC instrument was comprised of the same components described above for the 1D separations, including the use of the Discovery HS-F5 column as the firstdimension column. The outlet of the first-dimension column was connected to the inlet of the 10-port valve (Valco Instruments, Houston, TX) shown in the diagram of the complete 2DLC instrument shown in Figure 1. Both the 6- and 10-port valves were actuated pneumatically using helium at 70 psi. The two sample loops (loop 1 and loop 2 in Figure 1) used to alternately capture effluent fractions from the first-dimension separation and deliver them to the second-dimension column were 67-cm lengths ((0.2 cm) of 0.010-in.-i.d. PEEK tubing, such that the volume of each loop was 34 µL. A prototype eluent preheater and column heating jacket obtained from Systec Inc. (New Brighton, MN) were used to preheat the mobile phase delivered to the second-dimension column and maintain the column at 110.0 ( 0.1 °C. The column used in the second dimension was packed in-house with a prototype carbon-clad zirconia reversed-phase material (8% carbon, ZirChrom Separations, Inc.; Anoka, MN). The salient differences between the instrument described previously by this group18 and the present work are as follows: (1) the use of flow splitting in (47) Snyder, L. R.; Glajch, J. L.; Kirkland, J. J. Practical HPLC Method Development, 2nd ed.; Wiley & Sons: New York, 1996.
46
events start first-dimension gradient, inject sample in first dimension, start detector data acquisition start second-dimension gradient program on pump IIA switch 6-port valve to flush strong solvent from pump IIA and re-equilibrate second-dimension column with100% A solvent switch 10-port valve to inject fraction (from loop 2) from first dimension into second dimension start second-dimension gradient program on pump IIB switch 6-port valve to flush strong solvent from pump IIB and re-equilibrate second-dimension column with 100% A solvent switch 10-port valve to inject fraction (from loop 1) from first dimension into second dimension
a a and b are parameters that are adjusted to align gradient runs in consecutive second-dimension separations, typically 3.0 and 1.8 s in this work.
the first-dimension separation to reduce the effective gradient delay time and improve gradient reproducibility and (2) an the upgrade of the photodiode array detector (from HP1040A to G1315C), which allows a 10-fold increase in the rate of acquisition of UV-visible absorbance spectra. Absorbance spectra were collected at a rate of 80 Hz over the range of 200-600 nm at all time points of each 2DLC chromatogram. The HP 1090 pumps (binary pumps IIA and IIB in Figure 1) used in the second dimension of the 2DLC system consist of complete Series I DR5 pumping systems, such that each unit is capable of delivering solvent up to a flow rate of 5.0 mL/min at a pressure of 400 bar. Each second-dimension separation in the 2DLC separations consisted of a reversed-phase gradient from 0 to 85% B where the A solvent was 10 mM perchloric acid in water (pH ∼2) and the B solvent was pure acetonitrile. The total gradient cycle time was 21 s, with a gradient time (tg) of 17 and 4 s for re-equilibration of the HPLC column. The 4-s re-equilibration time corresponds to roughly two column volumes of solvent; one column volume is required to flush strong (ACN-rich) solvent out of the tubing between the six-port valve and the second-dimension column inlet, and the second column volume is required to actually re-equilibrate the HPLC column to the extent that the repeatability of retention time in the second dimension is satisfactory ((0.002 min standard deviation).18,44 LabVIEW 6.0 software and a 6024E data acquisition board (National Instruments Inc., Austin, TX) were used to control the coordination of the first-dimension HP 1090 system, the 6- and 10-port valves, second-dimension pumping systems, and photodiode array detector using simple programs written in-house. Table 2 gives the timing of all events required for two consecutive gradient elution cycles in the second dimension, starting from the very beginning of a complete 2DLC analysis. It is particularly important to note that the gradient programs of pumping systems IIA and IIB are started independently and the timing of these events is freely adjustable (a and b in Table 1 are the adjustable parameters, typically 3.0 and 1.8 s, respectively); this is an important factor in achieving satisfactory repeatability and matching of retention time in consecutive secondAnalytical Chemistry, Vol. 80, No. 1, January 1, 2008
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Figure 2. Percent error in gradient elution peak width prediction for 15-min 1D separation of low molecular weight mixture. Conditions are given in Table 1.
dimension gradient elution separations, as is discussed below. We also point out that the injection of fractions from the first dimension into the second dimension is delayed relative to the start of the second-dimension pump gradient program. This is done to effectively decrease the gradient delay volume of the second-dimension pumps to zero. The precision of retention time in consecutive second-dimension separations was discussed in detail in previous publications for 2DLC systems similar to the one described here.18,19 Precision of second-dimension retention time was evaluated from full 2DLC separations of the low molecular weight standard mixture (except riboflavin, which did not elute from the second-dimension column under the current conditions) discussed above. This mixture was also used to compare the precision of peak area in 1D separations and the analogous peak volume in 2D separations. The peak volume for a particular standard compound was calculated by summing the peak areas in all second-dimension separations (typically 2-5) containing a peak for that compound. RESULTS AND DISCUSSION Comparison of Predicted 1D and 2D Peak Capacities. To verify the accuracy of the model used to predict the first-dimension peak capacity upon which the following discussion is based, we injected the low molecular weight standard mixture under each of the experimental conditions and compared the experimental and predicted peak widths. As an example of these data, a plot of percent error in peak width for the 15-min 1D separation of the low molecular weight standards is shown in Figure 2. The predicted peak width values do not include a contribution from extracolumn broadening. As was discussed above, the extracolumn contribution is difficult to predict accurately, and our best estimate of the extracolumn variance indicates that it would contribute less than 10% of the total variance of peaks eluting under gradient conditions in all of the experimental conditions studied. The tyrosine peak observed by experiment is much wider than predicted (91%); we believe this large prediction error results from the fact that tyrosine elutes under primarily isocratic conditions. Analytes eluting under isocratic conditions are subject to significant broadening from the large injection volume used in this work (20 µL injected into a 2.1-mm-i.d. column) because they 274 Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
Figure 3. Predicted 1D (b) and 2D (O) peak capacity as a function of analysis time. 1D peak capacity is calculated using eq 1; 2D peak capacities are calculated using eqs 3-5, with the fraction of coverage term set to unity. The inset plot clearly shows that the 1D peak capacity does increase rapidly with increased analysis time at short analysis times but then begins to level off around 15-30 min.
are not focused. The effect of large injection volumes can be neglectedforanalyteselutingprimarilyundergradientconditions.39-41 The peak width for compounds eluting at times earlier than tyrosine will not be predicted accurately; however, this represents a very small part of the separation window because of the very small delay volume of the instruments used in this work. Indole3-propionic acid is the other compound giving a peak width significantly wider than predicted (49%). The peak shape for this compound is quite tailed despite the fact that varying the mass of the compound injected did not change the peak width. This suggests that the broad peak is probably not due to overloading, but is possibly due to the presence of a nearly coeluting impurity. All of the other standard compounds give peaks that are within a reasonable error (100 °C) for fast 2DLC because only a few stationary phases available for HPLC are thermally stable.9 Second, we want to emphasize the seriousness of the correction to the ideal 2D peak capacity to account for the broadening of first-dimension peaks due to the sampling process. In the case of the 60-min 2D separation, the first-dimension peak width (4σ) before sampling is ∼34 s, resulting in a broadening factor (eq 3) of 1.52, which is not too serious. However, at the 15-min analysis time, the first-dimension peak width (4σ) is just 12 s. With a second-dimension analysis time of 21 s, this results in a firstdimension broadening factor of 3.35 and a conditional 2D peak capacity of 302 compared to 136 for the 1D separation at the same analysis time. If the correction to the 2D peak capacity is not made and one simply assumes that the first-dimension peak capacity is equal to the number of fractions taken from the first-dimension effluent in the usable separation window (i.e., number of fractionlimited, 36 in this case), the 2D peak capacity is overestimated by more than a factor of 2, leading one to believe that the performance of the 2D separation is much better than it actually is. Figure 7 shows a comparison of first-dimension peak capacities computed by different methods. The solid and dashed lines give ideal (computed using eq 1) and number of fraction-limited estimates of 1nc. The dot-dashed (- ‚ -) line and the dotted (‚ ‚ ‚) line give undersampling-corrected estimates of 1nc, where the dotdashed line is corrected using the broadening factor calculated by Murphy et al.27 and the dotted line is corrected using the empirical broadening factor determined by Davis et al.29 The corrected 1nc given by the dot-dashed line is consistent with the results of a previous theoretical study by Horie et al.25 on the effect of undersampling on 2D peak capacity. Obviously the ideal and fraction-limited estimates grossly overestimate 1nc, especially at short analysis times, by more than 100% in some cases. The undersampling-corrected values give realistic estimates of 1nc, with the more accurate values given by correction based on the broadening factor determined by Davis et al. (see eq 3). Clearly
Figure 7. Plots of first-dimension peak capacities (1nc) computed by different methods. (s) Ideal 1nc computed using eq 1; no correction is made for first-dimension undersampling. (- -) Number of fractionlimited 1nc computed by simply counting the number of 21-s fractions of first-dimension effluent collected during the analysis. (- ‚ -) 1nc corrected for undersampling using eqs 1 and 4, and the broadening factor (1ws/1w) calculated by Murphy et al.25 (‚ ‚ ‚) 1nc corrected for undersampling using eqs 1 and 4, and the broadening factor determined by Davis et al.27 (eq 3); this method gives the most realistic and accurate estimate of 1nc for calculation of an effective 2D peak capacity. Table 5. Precision of Second-Dimension Retention Time, 1D Separation Peak Area, and 2D Separation Peak Volume 2t (s) R (s, n ) 2-4)
% RSD of peak area/volume
solute
average
SD
1D area
2D volumea
tyrosine 5-hydroxytryptophan tryptophan indole-3-acetic acid indole-3-propionic acid indole-3-acetonitrile
6.18 9.74 9.58 13.10 15.18 15.03
0.30 0.06 0.04 0.08 0.09 0.11
0.2 0.4 0.3 2.2 1.2 0.6
1.6 1.5 4.5 3.0 8.0 4.7
a Peak volume as measured by adding peak areas for a given component appearing in consecutive second-dimension separations.
the undersampling of the first dimension causes a serious loss in the conditional first-dimension peak capacity and, thus, in the conditional 2D peak capacity. Appropriate accounting for both undersampling of first-dimension peaks and the suboptimal utilization of the 2D separation space is the only way to give a fair and realistic comparison of 1D and 2D separations. Precision of 2D Separations. In previous reports on work using instrumentation similar to that described here, we reported the precision of first- and second-dimension retention time and peak volume.18,19 In the current study, we used the low molecular weight standard mixture to assess the precision of peak area in 1D separations and first- and second-dimension retention time and peak volume in 2D separations; these results are summarized in Table 5. As was observed previously,19 the first-dimension peak maximum for each component appeared in the same firstdimension fraction in replicate 2DLC separations of the low molecular weight standard mixture. This means the effective standard deviation of the first-dimension retention time is zero,
and thus, it is not reported in Table 5. We routinely observe excellent first-dimension retention precision in the short term (i.e., several consecutive runs); however the stability of firstdimension retention over the longer term (i.e., days) under the conditions described here is more problematic. Given the importance of good retention precision when multivariate data analysis algorithms are employed,48 stabilizing the first-dimension retention over the long term is of utmost importance and a major current focus of our work. The average relative standard deviation of second-dimension retention time (0.11%) is comparable to that found in our previous work, despite the larger range in seconddimension retention times analyzed compared to previous experiments. This represents a slight improvement in the repeatability of retention time in consecutive second-dimension runs. This was made possible by the change in the control scheme for the instrument shown in Figure 1, which allows continuous adjustment of the start time for the two binary pumps used in the second dimension and thus facilitates alignment of consecutive seconddimension separations. The average relative standard deviation of the 1D peak area was 0.8%. This is reasonable considering the manufacturer’s specification of 1.0%, which is evaluated under rather different conditions (1.0 mL/min, isocratic with water, no column attached) than those used for the 1D separations in this work. The analogous measure of the mass of analyte eluting from the system in a 2D separation is the peak volume, which we calculated by adding the peak areas for a given analyte appearing in consecutive seconddimension separations. The average relative standard deviation of peak volume was 3.9%, which is similar to a value we reported previously for 2DLC separations of peptides.18 We believe the increase in the variance of the peak volume measurement is not due to loss of analyte in the instrument or imprecise operation of instrument components, but rather is due mostly to the propagation of error associated with defining the integration window for several second-dimension peaks that contribute to a single peak volume measurement, as opposed to defining one integration window when making a peak area measurement in a 1D separation. CONCLUSIONS In this work, we developed a conceptual framework that is necessary for a fair and realistic comparison of the performance of 1D- and 2DLC separations as a function of analysis time. We then compared 1D and 2D separations of a low molecular weight extract of corn seed in terms of both predicted conditional peak capacities and the number of chromatographic peaks observed at 15-, 30-, and 60-min analysis times. The principal conclusions of this study are as follows: 1. Two significant corrections to the ideal 2D peak capacity are essential for a fair comparison of predicted 1D and 2D conditional peak capacities; (a) the ideal peak capacity is corrected by the fraction of the 2D separation space that is actually occupied by chromatographic peaks, and (b) the broadening of firstdimension peaks due to undersampling is considered, which effectively reduces the first-dimension peak capacity and thus the overall 2D peak capacity. (48) Fraga, C. G.; Prazen, B. J.; Synovec, R. E. Anal. Chem. 2001, 73, 58335840.
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1 2 no′ c,2D ) nc × nc × fcoverage ×
1
Ignoring these corrections can lead to overly optimistic conclusions about the performance of 2DLC compared to 1DLC. 2. Based on comparisons of both the predicted conditional peak capacities and numbers of peaks observed in experimental chromatograms, we conclude that 2DLC becomes superior to fully optimized gradient 1DLC for separations lasting more than ∼10 min (conservatively). This transition time is much shorter than intuitively expected, and we believe it will have a major impact on the role of 2DLC in liquid-phase separations in general. This work has focused on the development of a framework for comparing 1D and 2D separations and optimization of 1D separations and the first-dimension separations of the 2D system; a preliminary optimization of the second dimension of this 2D system was discussed previously.19 Future work involving the use of smaller particle sizes in 1D and 2D separations and further optimization of the second-dimension separation remain high priorities as part of a thorough and realistic comparison of the performance of 1D and 2D separations. Finally, we emphasize that the quantitative aspects of the observations in this work will undoubtedly be strongly dependent on sample type. This work
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has focused on the types of molecules expected in metabolomics applications and may be justifiably applied to closely related samples. However, we expect that the conclusions of a quantitative comparison of the performance of 1D and 2D separations for proteomics applications will likely be very different. Differences in the saturation of separations of metabolomic and proteomic samples, as well as the differences in the behavior of peptides compared to low molecular weight species under gradient elution conditions, will significantly impact the crossover point where 2D separation becomes superior to 1D separation. ACKNOWLEDGMENT This work was supported by a grant from the National Institutes of Health (GM54585), Fellowship from the American Chemical Society Division of Analytical Chemistry to D.R.S., and gifts from ZirChrom Separations (carbon-clad zirconia), Supelco (Discovery HS-F5 material), and Agilent Technologies (diode-array detector). The authors also thank Prof. Joe Davis for many helpful discussions.
Received for review August 7, 2007. Accepted October 9, 2007. AC701676B
