Anal. Chem. 1995,67, 885-890
Sample Multiplexing for Greater Throughput HPLC and Related Methods Charles P. Woodbury, Jr.,* John F. Fbloff, and Stacy S. Vincent Department of Medicinal Chemistry and Pharmacognosy (WC 781), Universiiy of Illinois at Chicago, 833 South Wood Street, Chicago, Illinois 60612-7231
We present a multiplexing scheme that pools samples for greater dciency in analysis. The method involves arraying the samples in a matrix and then pooling along rows and columns of the array. Sample pools are andyzed instead of individual samples. The content of a given sample is found by the intersection of a row pool with a column pool. Since this simple pooling scheme can lead to ambiguities in assignments when many samples have the same species, we also suggest a supplementary or augmented pooling scheme, involving the use of pools along diagonals across the sample array, to resolve the ambiguities. We demonstrate the pooling scheme, with resolution of some simple ambiguities, using HPLC for the analysis of fluorophore-labeled amino acids. The analysis of a large batch of samples by HPLC is constrained by the time required for making individual chromatograms for each sample. The chromatographyis timeconsuming and expensive in terms of reagents and disposal of waste mobile phase or eluent. Past schemes for increasing efficiency in sample throughput in chromatography have focused on using the column more efficiently, since at any given time only a small part of the column is actually engaged in chemically separating the injected solutes.’-3 Thus one might inject a second sample before all the peaks from a first sample have emerged from the column and hope to resolve unambiguously the peaks from the first sample from those of the second sample. This technique is, however, limited to samples whose components are already wellcharacterized.’S2 A different approach has been taken by some workers in molecular biology who are interested in characterizingclones in a recombinant DNA l i b r a ~ y . ~ Here - ~ one is again faced with analysis of a large number of samples by, for example, gel electrophoresis, and there is the same type of time constraint as that described above. A new sample multiplexing scheme used here involves putting the samples into a square array or matrix and then forming pools of samples by drawing aliquots of each sample in a given row or column of the array. In this way, any particular pool has only one sample in common with any other pool. (1) Murdock, H. R Anal. Chem. 1970,42, 687. (2) Macnaughtan, D.; Rogers, L. B. Anal. Chem. 1971,43, 822-826.
(3) Phillips, J. B. Anal. Chem. 1980,52, 468A-478A (4) Evans, G. K.; Lewis, K. A PYOC.Natl. Acad. Sci. U.S.A. 1989,86, 50305034. (5) Field, S. J. BioTechniques 1993,14, 531-532. (6) Zwaal, R R; Broeks, A; van Meurs, J.; Groenen, J. T.M.; Plasterk, R H. A Proc. Natl. Acad. Sci. U.S.A. 1993,90,7431-7435. 0003-2700/9510367-0885$9.00/0 0 1995 American Chemical Society
The pooled sample is then analyzed (e.g., by a hybridization assay? by electrophoresis of a restriction d i g e ~ t or , ~ by PCR amplification of the DNA fragment, followed by gel electrophoresi@), and the results are compared to those from all the other pools, both for rows and for columns in the array. A positive result for a “row pool” is matched to a similarly positive result for a “column pool”; the intersection of the given row and column then identifies the particular individual sample that is common to both pools. Pooling of the samples thus reduces the labor and expense of the analysis considerably. From our survey of the literature, it does not appear that this type of multiplexing has been applied to chromatographic analyses yet. One aim of this paper is to provide a practical demonstration of this multiplexing scheme in HPLC. However, there are false positive results that can arise as artifacts of the pooling scheme (see below). The suggested literature protocol for resolving these artifacts has been to analyze them individually.j In batches with a large number of ambiguous sample assignments, this need for serial analysis of individual samples can again be a severe constraint. We propose here an augmented pooling scheme that should be well-suited to analyzing sample batches that would show many ambiguous sample assignments under the original simple rectilinear pooling scheme. The method involves forming an additional two sets of sample pools, but the pools are now formed by selecting samples along diagonals across the matrix of samples. We apply this augmented pooling scheme to the analysis by HPLC of dansylated amino acids [dansyl, 5(dimethylamino)naphthalene1-sulfonyl], as a test of the multiplexing method. Despite the added complexity of the resulting chromatograms, we are able to resolve ambiguities and assign all samples correctly. Augmented Pooling Scheme. For purposes of method presentation we will consider a batch of 25 samples. Our actual experimental results were obtained with a smaller batch of 16 samples. The general principles remain the same, however, and can readily be extended to larger batch sizes as well. We form the 25 samples into a 5 x 5 array, marking the rows as A1-A5, and the columns by Bl-B5. Each sample lies at the intersection of just one row and one column and thus has a unique identification in terms of its row and column numbers. We can formally assign each sample a matrix location as an ordered pair of integers, corresponding to the row and column coordinates of the sample in the matrix. Sample pools are then formed by taking aliquots of each sample in a given row or in a given column. For example, a pool will be formed from all the samples in row A3, column B1, etc. Analytical Chemistty, Vol. 67, No. 5, March 1, 7995 885
c4
B1 B2 B3 B4 B5
Figure 1. An individual sample located at the intersection of a column pool and a row pool.
B1 B2 B3 B4 B5
Figure 2. Two column pools and two row pools intersect at four points, resulting in ambiguities in assigning true sample locations.
Each sample pool is analyzed; the results naturally cannot yet be assigned to individual samples. However, by comparing sample pool A3 with pool B1, we may note a component common to both pools (for HPLC, this might be a solute species eluting with the same value in both pools). Since pool A3 and pool B1 have only one sample in common, the sample having the matrix location (3,1), this identifies the sample containing the solute in question. This is illustrated in Figure 1. The same sort of logical analysis can be used for other solutes with different &values; the intersection of the row and column pools identifies the individual sample with that solute. This is the basic multiplexing scheme used by molecular biologists in their recombinant DNA work. However, it could easily happen that two or more samples would share a component that would of course migrate with the same R’value. For concreteness, suppose that sample (3,l) and sample (5,3) both have a component with the same &value. Then we will see this component in four pools: row pools A3 and A5 and column pools B1 and B3 (see Figure 2). Should the solute be assigned to the four samples identified by the intersection of the two rows A3 and A5 and two columns B1 and B3? No, because only two of these intersections are at samples that really contain this particular solute [samples (3,l) and (5,3)]; the other two intersections, at samples (3,3) and (5,1), are false positives that arise as an artifact of the pooling scheme. This drawback to the multiplexing scheme will only become worse as the batch size increases or the number of samples having common components increases. The effort required for individual 886 Analytical Chemistry, Vol. 67, No. 5, March 1, 1995
D3 D4 Figure 3. Pooling samples along diagonals resolve ambiguities from the row-and-columnpooling scheme.
sample analysis of all these ambiguous sample assignments could easily offset the efficiency gains made by adopting the multiplexing scheme in the first place. It is possible to resolve these ambiguitieswithout going to the extreme of individual sample analysis. This will involve setting up two more sets of sample pools. We will pool samples along diagonals across the sample array, running from the left to the right side of the array, and starting either from the top of the array or from the bottom. The diagonalswill be “wrapped around the array, so that each pool will contain five sample aliquots,just as before. Let us denote the pool formed from samples (l,l), (2,2), ..., (5,5) as pool C1; pool C2 contains aliquots from samples (1,2), (2,3), (3,4), (4,5), and (5,l); pool C3 contains aliquots from samples (1,3), (2,4), ..., (5,2), etc. There are five such pools in our 5 x 5 array. These pools are all formed along diagonals running from the top of the array downward to the right, “wrapping”around to the right side of the array. We then form another set of five sample pools by taking aliquots along diagonals rising from the bottom of the array, upward to the right. Let us denote the pool formed from samples (5,1), (4,2), ..., (1,5) as pool D1; we form four more such pools, again wrapping the diagonal around the array at the right side. Just as for the A and B pools, these new C and D pools are, in a sense, perpendicular to one another. By examining which of these diagonal pools have a solute in common, and by comparing that to our results with the vertical and horizontal pools, we can resolve the ambiguous assignmentleft by analysis of just the result from the vertical and horizontal pools. In the example of ambiguous assignments given above, four samples putatively held the solute in question but two of these were false positives. Using the diagonal pools, we find that pools C4, D3, and D4 contain the specified solute. This again identifies multiple samples (those at the intersections of the three diagonal pools), specifically samples (3,l) and (5,3). This is shown in Figure 3. At first glance it seems that we have gained nothing and perhaps have lost ground in identifyingthe proper samples, since we still have a total of four putative samples with the solute of interest. On comparing Figure 2 with Figure 3, however, we notice that only two samples appear at the intersections of sample pools in both sets, samples (3,l) and (5,3). And indeed, those are the proper samples with the solute of interest. Furthermore,
notice how the use of the diagonal pools also shows immediately that (3,3)and (5,l) are false positives. If these were true positives, then we would expect pools C1,C2,and D1 to exhibit the signal, but they do not. This confirms our identitication of samples (3,l) and (5,3) as the correct or true positives. Although we have based this discussion on a batch of 25 samples, this number was chosen mainly to show how the multiplexing scheme may be applied to large numbers of samples. The same principles would apply to either smaller or larger batches. EXPERIMENTAL SECTION
The organic solvents used in this experiment were Fisher Scientific HPLC grade toluene (Fairlawn, NJ), Mallinckrodt HPLC grade pyridine (Paris, KY), and Mallinckrodt glacial acetic acid. The mobile phase consisted of 150 mL of toluene, 50 mL of pyridine, and 3 mL of glacial acetic acid. This same mobile phase mixture was used to prepare the dansylated amino acid solutions. The solvent system used in these studies is that of Zanetta et al.,7 which was originally developed for thin-layer chromatography using silica gel. It is similar to solvent compositions used elsewhere8s9but with the less toxic toluene replacing benzene. All dansylated amino acids were purchased from Sigma Chemical Co. (St. Louis, MO). A standard 25 cm silica column from IBM Instrument Inc., a Waters Associates liquid chromatography pump Model M45 (Milford, MA), and an Applied Biosystems 980 programmable fluorescence detector were used in the analysis of the amino acid solutions. Operating pressure was approximately 500 psi, giving a flow rate of 1mL/min. The fluorescence detector was set at an excitation wavelength of 340 nm and an emission wavelength of 389 nm with a 25 nm slit width. A Goertz Metrawatt SE120 recorder was used at a rate of 0.5 cm/min for recording elution profiles. In preparing stock solutions, between 4.0 and 10.0 mg of dansylated amino acid or dansylamide was dissolved in 10-20 mL of the mobile phase, depending on sample solubility. Working solutions were 1:lOO dilutions of stocks. Before any sample was injected, a mobile phase blank of 20 pL was loaded to wash the column and to check for residual peaks. Then a 20 pL aliquot of the sample was injected and the elution followed for approximately 30 min. The column was then washed again as described above. Sample peak retentions were measured to the nearest 0.05 cm, relative to the point of injection. RESULTS
PreliminaryChromatographicCharacterization. Nineteen dansylated amino acids, along with dansylamide, were characterized for their respective relative retention times (Table 1). Sixteen different species were chosen to create a 4 x 4 array (as noted below, this is the “break-even” batch size). A second array, containing 14 different species (two species duplicated in the array), was made in order to test the augmented pooling scheme’s ability to resolve potential ambiguities. Nonambiguous Pool of Sixteen Samples. Sixteen different dansylated amino acids were made up as a 4 x 4 array, and eight (7) Zanetta, J. P.; Vincendon, G.; Mandel, P.; Gonbos, G. J. Chromatogr. 1970, 51, 441-458. (8) Deyl, Z.; Rosmus, J.J. Chromafogr. 1965,20,514-520. (9)Bayer, E.; Grom, E.; Kaltenegger, B.; Uhmann, R Anal. Chem. 1976,48, 1106-1109.
Table I. Retentlon of Dansylated Amino Acid Derivatives.
compound
mobility relative to dansyl amide
dansyl-NHz dansyl-Ile dansyl-Val dansyl-Nva dansyl-Pro dansylu-aminon-butyric acid dansyl-Phe dansyl-Met dansyl-Ala dansyl-Sar (I
1.00 0.96 0.90 0.87 0.80 0.78
0.73 0.68 0.65 0.61
compound
mobility relative to dansyl amide
didansyl-Lys N,O-didansyl-Tyr dansyl-Gly dansyl-Glu dansyl-Tw didansyl-(Cys)n dansyl-Thr dansyI-Hyp dansyl-Ser dansyl-Asp
0.58 0.56 0.39 0.39 0.38 0.36 0.36 0.27 0.27 0.24
Retention of dansylamide was 4.5 min or 2.25 cm.
Table 2. Peak Retentions In Pooled Samples, Using the Row-and-Column Pooling Scheme
sample pool A1
A2 A3 A4 B1 B2 B3 B4
peak 1 2.20 2.35 2.80 2.65 2.20 2.35 2.50 2.85
retention (cm) peak 2 peak 3 2.50 3.60 3.10 2.90 3.10 2.65 2.90 3.40
4.00 8.05 3.50 3.35 3.65 4.05 3.50 5.85
peak 4 5.80 9.75 6.30 5.50 5.45 6.35 9.85 8.10
different sample pools were made by pooling across rows or along columns, as described above. These eight sample pools were chromatographed as described in the Experimental Section. Each sample showed four sample peaks. Table 2 lists the amino acids used and summarizes the results. To match individual samples across sample pools, we compared retentions. A match was declared if two retention distances agreed within 0.1 cm (0.2 min at a flow rate of 1 mL/min); in most cases the retention distances were found to agree to within 0.05 cm. (This allowed finer discrimination among dansylated species with similar relative retentions compared to dansylamide.) We then constructed a table of these matches, ordered by increasingretention distance. Based on the row and column pool for the match, we deduced the individual’s sample position in the original 4 x 4 sample matrix. Additionally, individual sample identity was confirmed by reference to the average retention distance of pure compound. Table 3 presents these results and compares our deduced assignments with the true original matrix position of the individual samples. The slight differences in various retentions for mixture components, compared to those for the isolated components,we attribute to small changes in the constitution of the mobile phase over time. All samples were properly assigned. Ambiguous Pool of Fourteen Samples. The nonambiguous 4 x 4 array of samples did not test our alternative scheme for resolving ambiguities in positional assignment. To test this scheme, we constructed another 4 x 4 array in which two samples (dansylamide and dansylserine) were duplicated. (Compared to the first sample matrix, we have replaced dansylmethionine and dansyl-a-amino butyric acid with dansylserine and dansylamide, Analytical Chemistry, Vol. 67, No. 5, March 7, 7995
887
Table 3. Matrix Asslgnments of Individual Samples, for the Rowmand-ColumnScheme of Pooling
matched retention retention of pure values (cm) compd (cm)
1,4 3.2
2.20/2.20 2.35D.35 2.50/2.50 2.65/2.65 2.80/2.85 2.90/2.90 3.10/3.10 3.35/3.40 3.50/3.55 3.60/3.65 4.00/4.05 5.45/5.50 5.80/5.85 6.30/6.35 8.05/8.10 9.75/9.85
2.25 2.35 2.55 2.65 2.85 2.95 3.20 3.40 3.50 3.70 4.10 5.75 6.10 6.30 8.40 10.50
compound dansyl-NHz dansyl-Ile dansyl-Val dansyl-Nva dansyl-Pro dansyl-a-amino-n-butyric acid
dansyl-Phe dansyl-Met dansyl-Ala dansyl-Sar N ,O-didansyl-Tyr dansyl-Gly dansyl-Glu dansyl-Thr dansyl-Ser dansyl-Asp
Table 4. Peak Retentions In Pooled Samples, Using the Diagonal Pooling Scheme
retention (cm) peak3
sample pool
peak 1
peak 2
c1 c2 c3 c4 D1 D2 D3 D4
2.40 2.25 2.20 2.70 2.25 2.15 2.20 2.45
2.95 5.65 2.30 4.80 2.70 2.95 4.85 2.50
3.60 8.30 2.55 5.20 5.15 3.40 5.60 3.35
peak4 7.05 3.35 7.00 8.25 7.00 7.00 3.70
and have shuMed the positions of the various components.) This double replacement creates a number of possible ambiguities in assigning samples to their proper matrix positions. We then constructed eight sample pools along diagonals, as described above, and chromatographed these pools. Table 4 lists the amino acids used and summarizes the results. Pool C2 showed only three peaks, while the other seven pools all showed four peaks. As it turned out, pool C2 contained dansylamide as a replicate; hence, there were truly only three distinct components to be analyzed in this pool. To construct a table of sample assignments, we used the same matching criteria as before. Table 5 presents these results and compares our deduced assignments with the true original matrix position of the individual samples. In our analysis of these mixtures we noticed that dansylated amino acids eluting after dansylsarcosine showed greater mobility (eluted faster, with a shorter retention time) than in our experiments on the isolated dansyl amino acids. We believe this is due to small changes in the composition of the solvent over time. We also experienced difficulty in matching sample pools to identify dansylnorvaline. In this single case we relaxed our criterion of a matching retentions to within 0.1 cm and allowed a match that produced agreement in retention to within 0.15 cm. The ambiguities in assigning dansylamide and dansylserine were properly resolved and their true original matrix position deduced correctly (Table 5). Also, the other 12 amino acids were properly assigned. Again, individual sample identity was confirmed by reference to the average retention distance of pure 888 Analytical Chemistry, Vol. 67, No. 5, March 7, 7995
Table 5. Matrix Assignments of Individual Samples, for the Diagonal Scheme of Pooling
sample pools
matrix positions
C3 and D2 C2 and D1 C2 and D3 C3 and D4 C1 and D4 C4 and D1 C1 and D2 C3 and D2 C3 and D4 C1 and D4 C4 and D3 C4 and D1 C2 and D3 C4 and D3 C1 and D2 C2 and D1
2,4 and 4,2 2,3 and 4,l 1,2 and 3,4 1,3 and 3,l 2,2 and 4,4 1,4 and 3,2 1,land 3,3 2,4 and 4,2 1,3 and 3,l 2,2 and 4,4 2,l and 4,3 1,4 and 3,2 1,2 and 3,4 2,l and 4,3 1,l and 3,3 2,3 and 4,l
retention of pure values (cm) compound (cm) compound matched retention
2.15/2.20 2.25/2.20 2.25/2.25 2.30/2.45 2.40/2.50 2.70/2.70 2.95/2.95 3.40/3.35 3.35/3.35 3.60/3.70 4.80/4.85 5.2/5.15 5.65/5.60 7.00/7.00 7.05/7.00 8.30/8.25
2.35 2.25 2.25 2.60 2.50 2.80 3.10 3.70 3.45 4.10 5.75 6.10 6.30 8.40 8.40 10.5
dansyl-Ile dansyl-NHz dansyl-NHz dansyl-Nva dansyl-Val dansyl-Pro dansylPhe dansyl-Sar dansyl-Ala
dansyl-Tyr dansyl-Gly dansyl-Glu
dansyl-Thr dansyl-Ser dansyl-Ser
dansyl-Asp
compound. We conclude that our pooling scheme is indeed working correctly. DISCUSSION
The selection of the system to test the multiplexing scheme was based on the availabilityof an HPLC apparatus from a student instructional laboratory, equipped with a used normal column. The success of the multiplexing scheme in identifying samples even in a small pool impressed us. The scheme worked well, despite the reduction in column efficiency by manual sample injection in place of automated injection and despite our use of a well-used column from a student laboratory instead of a new high resolution column. Considering the analysis of larger batches versus small batches, it may be more convenient and efficient to run individual samples if the batch is small. The break-even point actually occurs for a batch size of 16, formed into a 4 x 4 array. Using all four types of sample pools, we would have to form 16 such pools in total, for a complete application of the augmented multiplex method. This of course equals the number of individual serial analyses that would have to be performed on the batch, so nothiig is gained here. However, for batches larger than 16, the method quickly becomes more efficientthan individual sample processing. The efficiency advantages of the multiplexing scheme can be formulated as follows. For an N x N array of samples, one would have to run a total of N2 individual sample analyses. However, one would need to run only 4N analyses using the augmented pooling scheme. For a batch of 100 samples in a 10 x 10 array, this amounts to running only 40 assays on pooled samples versus 100 assays on the unpooled, individual samples. The time and quantity of reagents have been reduced by a factor of 2.5. Furthermore, this advantage increases as the size of the batch increases. For especially large batches, it would be possible to construct a three-dimensional array and apply a suitably modified multiplexing scheme for even greater efficiency (see Zwaal et a1.9. For instance, forming a batch of N3 samples into a cube, N x N x N , suggests taking sample pools composed of entire “layers” in the cube, and assaying the layers instead of individual samples. A batch of R” samples could then be surveyed with just 3N assays. The location of an individual sample is located by the intersection
of the corresponding three layers, corresponding to Cartesian x, y, z coordinates. There might again be ambiguities in sample assignments, but an augmented pooling scheme using diagonal layers could then be applied to resolve them. A total of 6N such diagonal pools should resolve ambiguities in locations. Thus a total of 9N assays would be required for a batch of h" samples. The break-even point in batch size occurs when h" = 9N, or a cubical array of 27 samples that is 3 x 3 x 3. The gains in efficiency can be quite large. Consider, for example, a batch of 1000 samples. Forming a cubical array and employing the suggested method of pooling samples across layers will reduce the number of assays from 1000 individual assays to as little as 30 assays, if no ambiguities in locating samples arise, or to 90 assays if diagonal layer pools are used. Returning to the planar arrays, there are some practical limits to the method's applicability. For example, from an informal check of 4 x 4 and 5 x 5 matrices, it appears that, for square matrices with an odd number of rows or columns, these diagonal pools will intersect just once with each other. For an even number of rows or columns, however, they may form two intersections. This double intersection may be another source of ambiguity in assigning samples to the proper matrix location. Column capacity will set an upper liiit to the number of samples that may be pooled together. The number Nof samples per pool can be estimated by dividing the column capacity by the mass of the average sample aliquot. For example, if the column capacity were 50 mg, and each sample aliquot contained 5 mg on the average, then clearly we should not form pools of more than 10 samples. In this particular example the multiplexing scheme would be limited to a total batch of 100 samples in a 10 x 10 array. Because columns with high efficiency generally have low capacities, this may be an important consideration in applying the multiplexing scheme to large batches of samples. Furthermore, successful detection of the component of interest in a pool of a large number of samples will require a sensitive method suited to analysis of dilute samples. The dilution of individual sample aliquots in forming the pools may limit the application of the multiplexing scheme. If the minimum acceptable signal intensity for detecting a component is &in and the original sample would produce a signal intensity of S, then the sample can be diluted only by a factor of S/Smi,. This dilution factor then is an upper bound to N, the number of samples in a pool. There may also be some dif&iculties in resolving ambiguities in samples with multiple components. This will depend on how well the system has been optimized to resolve different components. Clearly, some effort must be expended in finding conditions to reduce the possible coelution or overlap of peaks from different components. Since the time needed for optimization will vary considerably from system to system, we cannot predict beforehand in detail how much savings in time and effort may be realized by applying the pooling scheme, compared to the time and effort needed for system optimization. We will set aside this question, since our focus here is on improving sample throughput. Consider the following example of the savings in time that are possible with the pooling scheme. With an autosampler and automated injection system one might expect sample pooling to require only a few seconds,while sample run times on the column might be in the range of minutes to tens of minutes. For a batch
of 100 samples and an average run time of 10 min, the total time needed for individual analysis of all the samples would be 1000 min. Use of the augmented pooling scheme would call for 40 sample pools, requiring a total of 400 min running the column. If we allow 50 min for forming sample pools (at the very slow pace of a 0.5 min per sample), the pooling scheme saves 550 min over individual analyses. A more subtle limitation to the pooling scheme arises from the possible random overlap of component peaks in a chromatogram. Davis and GiddingslO have shown that in a random chromatogram, relative to the maximum possible number of peaks, there will be a discouragingly large number of overlapping component peaks. They also have shown that there must be approximately 95%vacancy (5%of the peak capacity used) in order to give a 90% probability that a given component will appear as an isolated peak and not overlap with another component. This would seem to imply that for a batch of 100 samples with each sample containing a single component we must use a column with a capacity for 2000 peaks to reach 5% of the peak capacity and have a 90%probability that the peaks are truly isolated. However, in our pooling scheme for this batch size we need only to compare two sample pools of 10 samples each, i.e., a total of 20 samples. This greatly reduces the demand on column peak capacity from 2000 to 400, a much more reasonable number. Giddings" has presented a formula relating the peak capacity n,, the number of theoretical plates on the column N, the column void volume Vo,the maximum practical retention volume V,,, and the resolution R,:
A reasonable estimate for VmJVo might be about 7; a useful value of R,is 0.5. With these values, we have the approximate relation
n, = f i For a comparison of 20 components (two sample pools of 10 components each), this suggests that we use columns with 1.6 x lo5 theoretical plates in order to meet the 5% peak capacity criterion. Doubling the pool size (quadrupling the overall batch size from 100 to 400) would call for a column with 6.4 x 105 theoretical plates. This is certainly a very large number, but it is not impossibly large, given the recent advances in HPLC and capillary zone electrophoresistechniques. Furthermore, one can try to raise the ratio VmalVo by manipulating flow rates, solvent composition, and so on, and so reduce the number of theoretical plates required. There will always be a number of false positives that arise in our pooling scheme simply by the chance overlap of a peak from one pool with a peak from another pool. As discussed above, this can be reduced by using only a fraction of the column capacity. Furthermore, the augmented pooling scheme could serve to reduce this further since peaks are assigned to each sample by two separate pool comparisons. It is unlikely that the same sample will be misidentified by chance (due to random peak overlap) in two separate sets of pools. (10) Davis, J. M.: Giddings, J. C. Anal. Chem. 1983,55, 418-424. (11) Giddings, J. C. Anal. Chem. 1967,39, 1027-1028.
Analytical Chemistry, Vol. 67, No. 5, March 1, 1995
889
For large batches of simple single-component samples, the multiplexing scheme described here offers substantial increases in sample throughput. We have demonstrated the method using a manual injection system and a well-used column. This method would seem to be very acceptable for automation on current systems with high efficiency columns, autoinjection of samples, and software-driven data analysis.
The augmented pooling scheme described here is not limited in application to HPLC systems or indeed to separation methods in general. The row-and-column scheme of sample pooling has already found several applications in molecular biology in assays not involving any ~hromatography.~-~ We urge consideration of the augmented pooling scheme whenever there is a large batch of samples to analyze.
CONCLUSION
ACKNOWLEDGMENT
With respect to the multiplexing scheme, we found that for a 4 x 4 array of 16 different samples our scheme correctly assigned all samples to their proper locations, without requiring us to analyze individual samples. A 4 x 4 array of 14 different samples, with two samples represented twice, was also correctly resolved using the augmented pooling scheme, despite some minor difficulties with solvent compositional changes affecting solute mobilities.
890 Analytical Chemistry, Vol. 67, No. 5, March 1, 1995
We thank Wenda Ramos, NIH 1992 Minority High School Student Research Apprentice, for preliminary investigation of solvent systems for the HPLC separations. Received for review May 31, 1994. Accepted December 19, 1994.@ AC940552Y Abstract published in Advance ACS Abstracts, February 1, 1995.
