Fourier Transform Capillary Electrophoresis with Laminar-Flow Gated

Aug 3, 2007 - To illustrate experimentally the improvement offered by FTCE in S/N ratio and resolution, we carried out a modest number (five) of multi...
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Anal. Chem. 2007, 79, 6807-6815

Fourier Transform Capillary Electrophoresis with Laminar-Flow Gated Pressure Injection Peter B. Allen, Byron R. Doepker, and Daniel T. Chiu*

Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195

Fourier transform capillary electrophoresis (FTCE) was developed as a method to improve signal-to-noise ratio (S/N) and resolution in capillary electrophoresis (CE) separation. In FTCE, multiple simultaneous CE separations were performed in the same channel system and interrogated using a single-point detector. To illustrate experimentally the improvement offered by FTCE in S/N ratio and resolution, we carried out a modest number (five) of multiple injections and separations. We show even with this small number of separations, S/N increased by a factor of 2.9, and theoretical plate height improved by a factor of more than 30. We demonstrated this technique with laser-induced fluorescence detection, but a wide variety of detection methods are compatible with FTCE. To improve signal-to-noise ratio (S/N) and resolution in separation, correlated detection using multiple-point detectors,1 Hadamard transform,2,3 and Fourier transform (FT) of data from arrays of detection points4-6 have been demonstrated. Using a different approach, this paper describes a concept we termed Fourier transform capillary electrophoresis (FTCE), which adds to the range of techniques that bring to bear frequency-domain computational power on physical separation and detection. This strategy is particularly advantageous as it is easily adaptable to any point-detection scheme and does not require the use of array detectors. Manz and co-workers have produced a body of work on the subject of frequency-domain detection,4-9 which uses principles similar to those employed here. For example, they have analyzed the complex output from a sequence of fluorescence-detection points7 and employed wavelet transform to the analyses of these outputs.10 Similarly, Shippy and co-workers exploited the spatial resolution offered by imaging and used Shah convolution Fourier * To whom all correspondence should be addressed. E-mail: [email protected]. (1) LeCaptain, D. J.; Van Orden, A. Anal. Chem. 2002, 74, 1171-1176. (2) Guchardi, R.; Schwarz, M. A. Electrophoresis 2005, 26, 3151-3159. (3) Kaneta, T.; Kosai, K.; Imasaka, T. Anal. Chem. 2002, 74, 2257-2260. (4) Kwok, Y. C.; Manz, A. J. Chromatogr., A 2001, 924, 177-186. (5) Kwok, Y. C.; Manz, A. Analyst 2001, 126, 1640-1644. (6) Kwok, Y. C.; Manz, A. Electrophoresis 2001, 22, 222-229. (7) Crabtree, H. J.; Kopp, M. U.; Manz, A. Anal. Chem. 1999, 71, 2130-2138. (8) Mogensen, K. B.; Kwok, Y. C.; Eijkel, J. C. T.; Petersen, N. J.; Manz, A.; Kutter, J. P. Anal. Chem. 2003, 75, 4931-4936. (9) Yang, X.; Jenkins, G.; Franzke, J.; Manz, A. Lab Chip 2005, 5, 764-771. (10) Eijkel, J. C. T.; Kwok, Y. C.; Manz, A. Lab Chip 2001, 1, 122-126. 10.1021/ac0710026 CCC: $37.00 Published on Web 08/03/2007

© 2007 American Chemical Society

transform to improve the S/N of the detected peaks.11 Another strategy is to employ a circular separation system in which sample is repeatedly circulated and detected.9 In all of these cases, the sample is repeatedly or constantly illuminated over the course of separation and is examined in such a way as to yield a periodic signal that can be processed in the frequency domain. Any of these strategies can increase the S/N of the detected fluorescence signals. Many of these techniques, however, require the ability to carry out multiple detections (e.g., by fluorescence imaging) along the length of the separation channel. With optical detection, multipoint or image detection is relatively easy; it requires only limited modification to existing fluorescence apparatus. This fact does not transfer to nonoptical methods of detection (e.g., electrochemical detection); in such cases, multipoint detection may require elaborate or tedious mechanisms. Because of this practical need for multipoint detection, fluorescence imaging is deeply embedded in many of these frequency-domain analyses. Yet, laserinduced fluorescence (LIF) can achieve impressive detection limits down to the single-molecule level,12 without any enhancements using frequency-domain techniques. As a result, other modes of detection are more likely to benefit from the gains offered by frequency-domain methods, and for these applications, single-point detection is likely the most appropriate and practical. One strategy to approach such frequency-domain analysis using single-point detection is to modulate injection according to a particular sequence such that the output can be processed using the Hadamard transform2,13 or correlation.14 The main drawback of this approach is the added complexity: modulated injection requires complicated fluidics15 or electronics2 or both;16 optical uncaging requires special labeling and (typically) a second laser, although single-laser techniques have been used for optical gating.17 To address this drawback, this paper describes a method that employs parallel injection for achieving frequency-domain enhancement of separation resolution and S/N of the detected peaks. Our approach rests on the ability of the microfluidic chip (or other separation arrangements) to produce a series of linearly spaced peaks for each analyte in the sample with a periodicity determined by its mobility. It is illustrative to conceptualize as a (11) McReynolds, J. A.; Edirisinghe, P.; Shippy, S. A. Anal. Chem. 2002, 74, 5063-5070. (12) Schiro, P. G.; Kuyper, C. L.; Chiu, D. T. Electrophoresis 2007, (in press). (13) Kaneta, T.; Kosai, K.; Imasaka, T. Anal. Sci. 2003, 19. (14) Fister, J. C.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1999, 71, 44604464. (15) Bu ¨ ttgenbach, S.; Wilke, R. Anal. Bioanal. Chem. 2005, 383, 733-737. (16) Hata, K.; Kaneta, T.; Imasaka, T. Anal. Chem. 2004, 76, 4421-4425. (17) Kaneta, T.; Yamaguchi, Y.; Imasaka, T. Anal. Chem. 1999, 71, 5444-5446.

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series of n plugs of sample in a single capillary with uniform physical spacing. Upon electrophoresis, each analyte in the sample will be represented n times at the detector. Because all of the n plugs of any given analyte travel at the same rate, the peaks will arrive at the detector at periodic retention times with a frequency proportional to the total velocity of that analyte. Since the peak system for each analyte is periodic, it gives a signal in the frequency domain that is characteristic of its velocity. Our physical implementation aims for the same result but differs (for reasons of technical simplicity) in that we fabricated multiple separation channels of increasing lengths that converge into a single channel (where detection takes place) rather than a single channel with multiple injections. We chose an injection mode that was simple and efficient, relying on laminar flow and fluidic resistance to produce a set of injected sample plugs in the set of microfluidic separation channels. It is similar to the work of Solignac and Gijs18 but simplified to remove the need for a membrane or electromechanical actuator. Our approach is easily applicable to any singlepoint detector setup, including fluorescence,19 thermal lens,20 electrochemical,21 or contactless conductivity detection.22 The first advantage of FTCE is the improvement in S/N of the detected peaks compared to a single channel. The increase in S/N gained by running n separations in parallel is equivalent to that gained by averaging n independent runs. The second advantage is the improvement in resolution compared to a single channel. Peaks need not have baseline separation in the time domain in order to be resolved by a fitting routine in the frequency domain. The effective resolution also improves with the length of the data set to which the FT is applied; thus, the resolution also scales with the number of channels. As a final advantage, the FT acts as a data reduction technique to simplify computation. The performance of nonlinear fitting routines is significantly increased in the frequency domain because the relevant number of data points is reduced. MATERIALS AND METHODS Preparation of Labeled Amino Acids. We prepared fluorescein isothiocyanate (FITC)-labeled amino acids (glycine, glutamate, aspartate) according to the manufacturer’s instructions (Invitrogen). Briefly, we dissolved each amino acid at 1 mM concentration in 100 mM carbonate buffer at pH 8.5. We dissolved FITC in DMSO at 1 mg/µL and added it to carbonate buffer for a final concentration of 1 mg/mL. The solution was allowed to react for 3 h with mixing and then was refrigerated. Just prior to use, each of the labeled amino acids was mixed at a ratio of 1:1:1 and diluted by a factor of 100 into 50 mM borate buffer at pH 9. Chip Design and Fabrication. We designed our chip such that the injection points and exit points of the five microchannels are adjacent to one another in order to ensure that the voltage applied across each channel is nearly identical. We included five (18) Solignac, D.; Gijs, M. A. M. Anal. Chem. 2003, 75, 1652-1657. (19) Kuo, J. S.; Kuyper, C. L.; Allen, P. B.; Fiorini, G. S.; Chiu, D. T. Electrophoresis 2004, 25, 3796-3804. (20) Seidel, B. S.; Faubel, W. Biomed. Chromatogr. 1998, 12, 155-157. (21) Martin, R. S.; Gawron, A. J.; Lunte, S. M.; Henry, C. S. Anal. Chem. 2000, 72, 3196-3202. (22) Pumera, M.; Wang, J.; Opekar, F.; Jelinek, I.; Feldman, J.; Lowe, H.; Hardt, S. Anal. Chem. 2002, 74, 1968-1971.

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channels with lengths that increase according to a square root (2.24, 2.41, 2.57, 2.72, 2.86 cm) to compensate for the quadratic dependence of retention time on channel length. We produced our chips by replicating poly(dimethylsiloxane) (PDMS) from a SU-8-on-silicon master, which was fabricated using two-layer photolithography. This procedure has been described extensively elsewhere.23 Briefly, photomasks with the desired channel designs (Figure 1A) were drawn up in Macromedia Freehand and generated using photoplotting (Photoplot Store, Colorado Springs, CO). Prior to photolithography using the photomask, SU-8-2025 photoresist (Microchem, Newton, MA) was spin-coated onto a silicon wafer at 20-µm thickness to form layer 1 features on the silicon wafer (Figure 1A). Following exposure, curing, and development of this layer 1 feature, SU-8-2100 was spin-coated onto the same wafer at 100-µm thickness and exposed using a second photomask to define the features for layer 2 of the SU-8on-silicon master. Features of the two layers were aligned and exposed to UV light with a mask aligner. Following curing and development, the finished two-layer master was coated with (tridecafluoro-1,1,2,2-tectrhydrooctyl)trichlorosilane (Gelest, Morrisville, PA) by gas-phase deposition to prevent sticking of PDMS during molding and peel-off. The molded PDMS replica was punched with holes to define reservoirs for fluid inlets and outlets, after which the PDMS mold was permanently sealed to glass via exposure to oxygen plasma. Injection of Sample into Separation Channels. We connected the finished microfluidic chip to two separate syringes held in a syringe pump (KD Scientific, Holliston, MA) using polyethylene tubing. Although pressure could be applied by one syringe, we chose to use two because a single syringe connected to both the inlet and outlet channels would be connected to both the high voltage and ground, creating a short circuit that would change the electrical characteristics of the chip. The pump pushed 50 mM pH 9 borate buffer into the chip (at locations labeled “buffer inlets” in Figure 1B) and through the inlet channel and waste channel at a nearly constant rate of 15 µL/min. The inherent pressure capacitance of the elastomer and polyethylene tubing allows for some modulation of the velocity of pressure-driven flow. Using a separate, micrometer-actuated syringe connected to the sample channel, we applied high pressure to drive sample into the sample inlet channel (labeled “sample inlet” in Figure 1B) and across to the separation channels, taking advantage of the capacitance of the system and briefly interrupting the flow of separation buffer. RESULTS AND DISCUSSION Injection and Plug Formation. We fabricated a microfluidic chip (Figure 1) to produce a series of linearly spaced peaks after separation for each analyte in the mixture. If an equal voltage (v) is applied across all channels, then the peak retention time (tn) will scale with the square of the channel length. This follows from the fact that the distance the analyte must travel is proportional to the length (Ln) of the nth channel, and the speed at which the analyte travels is proportional to its mobility (µ) multiplied by the (23) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974-4984.

Figure 1. Schematic showing the channel design and experimental setup. (A) The photomasks we used for fabricating layer 1 (upper left) and layer 2 (upper right) of our two-layer microfluidic system. (B) Layout of our experimental apparatus with respect to the microfluidic separation channels.

voltage gradient (E). This is illustrated by the following relationship:

tn )

Ln Ln Ln2 ) ) v Eµ Vµ

As a result, the channel lengths in the sequence must scale according to a square-root progression to yield uniform peak spacing from each analyte. We build our device and simulations on a series of lengths that are the square roots of the components of the following linearly increasing series, 5, 5.8, 6.6, 7.4, 8.2, which are given (in cm) by Ln ) {2.24, 2.41, 2.57, 2.72, 2.86}. All channels converge into a single channel such that all separated analytes pass through a single common detector region (Figure 1). Our approach is unique in that multiple injections are carried out simultaneously to produce analyte-specific periodicity, which differs from the work of Kwok et al.6 in which multiple sample plugs are electrokinetically injected into the same channel at different times. While multiple injections in time may increase the signal from a detector already designed to produce a periodic

signal, it cannot produce a unique frequency signal for each analyte because the periodicity in time of elution will be equal to the periodicity in time of injection for all analytes. The implication of this difference for the experimental design presented in this paper is that a user may (in principle) carry out the parallel injection sequentially several times to further increase the S/N. The model function used by the fitting routine would require modification to account for the new pattern generated at the detector, but the notion suggests that further performance increases could be attained without modification of the physical chip design. Figure 2 shows the procedure we used to achieve simultaneous parallel injection. Figure 2G shows the layout of the large and small channels of the chip in bright field. The large channels at left are 200 µm wide and ∼100 µm tall. These comprise the inlet channel and sample channel, which join in a “T” configuration (see schematics at the left side of the figure). The five small channels to the right are 20 µm wide and ∼20 µm tall and comprise the separation channels. Figure 2H is an epifluorescence micrograph showing the initial laminar boundary between clear Analytical Chemistry, Vol. 79, No. 17, September 1, 2007

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Figure 2. Illustration and experimental images showing the procedure for achieving laminar-flow gated parallel pressure injections. (A-F) are schematics where the arrows indicate direction of flow and the relative applied pressures. (G-L) are the corresponding experimental images taken in bright field (G) and fluorescence (H-L). To achieve injection, laminar flow is first established (A), after which pressure from the sample stream is increased progressively (B-D) to displace the buffer stream and so the sample stream can make contact with the set of parallel separation channels (E). After sample has been introduced into the separation channels, pressure from the sample stream is reduced so that the buffer stream can efficiently wash away the residue samples in the large channel (F). Scale bar in (H) is 200 µm.

borate buffer (right stream) and fluorescent sample (left stream) under illumination with a solid-state 488-nm laser (see corresponding schematic in Figure 2B). In these images, the sample contained Alexa 488 dye. The laminar boundary between the flow from the inlet channel (which is labeled Buffer in Figure 2B) and 6810

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from the sample channel (which is labeled Sample in Figure 2B) was shifted by modulating the applied pressure to the sample channel (see Figure 2C and I and D and J); the fluorescent stream visibly became wider. By applying a short and sudden increase in pressure to the sample channel, we brought the boundary of

Figure 3. Simulated five-channel electropherograms for a single analyte (top panels) and a portion of the corresponding absolute value of the Fourier transforms (bottom panels), in the absence of noise (A) and in the presence of added Poisson noise (B).

the sample stream into contact with the separation channels and thus effected injection (see Figure 2E and K). After injection (see Figure 2F and L), the buffer from the inlet channel re-established laminar flow and severed the sample stream from the separation channels. Once the sample plugs were introduced into the separation channels (Figure 2L) and any residual sample was washed down into the waste well, 1 kV was applied to initiate separation (Figure 1B). The detection region was illuminated with focused 488-nm light (Coherant Sapphire) and the fluorescence measured with a single pixel of a CCD camera (PhotonMax, Princeton Instruments). This injection scheme is particularly well suited for FTCE as it is very simple to implement, although less precisely controlled than electrokinetic injection. The lack of precise automated control may produce some variability in plug size from run to run, but the FT mode of detection minimizes the impact of this variability by looking at periodicity rather than the shape of individual peaks. Results from PDMS chips are difficult to make reproducible; extensive pretreatment has been explored as a remedy.24 As such, the precision of computer-controlled electrokinetic injection may not be the limiting factor for such devices. In that case, a less stringent but simpler technique such as is presented here may be useful. Simulation and Interpretation of Periodic Electropherogram. To show the basic functionality of the FTCE strategy and to characterize its performance, we employed numerical simulations. We first simulated a series of peaks for a single analyte eluted from five channels of increasing length. Total velocities of the analytes were simulated as constant and proportional to the (24) Vickers, J. A.; Caulum, M. M.; Henry, C. S. Anal. Chem. 2006, 78, 74467452.

applied voltage gradient. The simulated channel lengths were consistent with experimental design: 2.24, 2.41, 2.57, 2.72, and 2.86 cm. Electrophoretic mobility was arbitrarily chosen to give a retention time of 18 s through the shortest channel. We compared the results of the absolute value of the discrete Fourier transform (DFT) of the five resulting peaks without noise (Figure 3A) to that produced after adding Poisson noise (Figure 3B). The improvement in S/N is evident in Figure 3B, where the S/N in the time domain (top panel) was 3.2, which improved to 7.3 in the frequency domain (bottom panel). As expected, the pattern generated in the frequency (or Fourier) domain was not a single peak (see Figure 3A bottom panel) when applying the DFT to the periodic (but not sinusoidal) simulated peak pattern in Figure 3A,B (top panels). While a fundamental frequency and several harmonics are visible when the absolute values of the DFT data are shown (see Figure 3), in many circumstances, the raw DFT data are not necessarily informative to simple inspection. While other groups have treated this problem using alternative transformations,10 we treated this problem by using a multivariate fit of a set of appropriate basis vectors to the DFT data. This set of basis vectors was made from a range of simulated separations generated as a function of the mobility of the simulated analyte. Because the salient parts of the DFT data are represented in the lower frequencies, we could safely omit the high-frequency data when performing the fit, thus reducing the processing time considerably. Figure 4 shows the results of this basis-vector optimization and data-fitting strategy. Figure 4A shows how a simulated singleanalyte sample (top panel) eluted from five separation channels Analytical Chemistry, Vol. 79, No. 17, September 1, 2007

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Figure 4. Simulated five-channel electropherograms for one analyte (A) and for two analytes (B). Top panels are simulated electropherograms prior to addition of noise, and middle panels show the electropherograms after Poisson noise has been included. Bottom panels show the improvements offered by Fourier transform and the accompanying data analysis. Squares represent the coefficients of the basis vectors, and the solid line is the best-fit Gaussian curve.

is buried in noise (middle panel). From these simulated highnoise separation data, 600 points (which correspond to 60 s of real data as acquired by our detection scheme) were selected and transformed with the DFT. We note the real component of the DFT of the data as Data′ν in terms of frequency component ν. To interpret the DFT of these simulated data, we compared it against the DFT of a set of simulations using a basis-vector optimization routine (developed in-house using Mathematica). The optimization routine starts by generating simulations of single-analyte, fivechannel separations in a manner similar to the original simulation in the top panel of Figure 4A; each simulation, St in terms of time (t) at a sample frequency of 10 samples/s, models a single analyte through five channels where the calculated peak retention times are given by tn and produces a system of five linearly spaced peaks. A set of 600 mobilities, µi|i){1-601}, are each used to generate a 6812

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simulation. Each simulation St,i is thus a sum of five Gaussian distributions given by the following equation:

St,i )

2

5

e(-(1/2σ )[t-tn]

n)1

x2π σ

∑

2

Once the DFT is applied to each of these simulations, the real component of points 2- 60 are selected, which represent putative sinusoidal frequency components of the data with a peak-to-peak period that ranges from 60 to 1 s. We note the real component of the DFT of St as S′ν in terms of frequency component ν. We treat these partial DFT simulation data sets, S′ν,i, as basis vectors. The real components of the DFT of the original simulated data to be fit (Figure 4A middle panel) are treated as a linear combination

Figure 5. Experimental measurements and the accompanying simulations showing the raw electropherogram obtained after the separation of four analytes using five channels. In the top trace, squares represent the experimental data and the solid line is the best-fit curve. The four lower traces are simulations showing the retention times for each of the analytes present, to help illustrate the origin of each of the 20 peaks in the top trace.

of these basis vectors, where each basis vector (in terms of i) is multiplied by a coefficient, C, and then the products are summed. The set of these coefficients is a coefficient vector Ci. Each element of the coefficient vector corresponds to the relative “weight” or abundance of a substance moving through the channel system. We optimize the coefficient vector to minimize F, the sum of the absolute value of the differences between the weighted linear combination of the basis vectors and the DFT of the simulated real data: 60

F)

∑ (| ∑ 〈C S′ i

υ)2

u,i〉

- Data′u|)

i

The optimization of F is accomplished using a custom maximum slope, Monte Carlo method. The result of the basis vector optimization routine is this optimized coefficient vector Ci. We have included a Mathematica notebook file containing the minimization routine as Supporting Information. Each simulated substance has some particular mobility and, consequently, some particular retention time through a single channel under a chosen set of conditions. For simplicity, we may therefore represent the optimized coefficient vector that is the result of the basis-vector optimization routine in terms of the retention time from a channel of a length equal to the last single channel in the series (2.86 cm) under an applied voltage of 1 kV. We ran the basis-vector optimization routine 50 times from randomized starting points and averaged the results. The resultant average coefficient vector is shown in the bottom panel of Figure

4A in terms of the elements’ respective equivalent retention time. One peak can be seen; it represents the single analyte in the system and corresponds to the peak eluting from the 2.86-cm channel in the original simulated separation. Figure 4B shows the results of applying the same basis-vector optimization routine to a two-analyte system where even the fifth and longest capillary in the simulation does not yield baseline separation (right-most peaks in top panel of Figure 4B). As before, we buried this signal under considerable Poisson noise and applied the same basis-vector optimization routine, which revealed two clear, fully resolved peaks with much improved S/N. Results from FTCE Separation Chip. We then implemented FTCE experimentally to confirm the results of our simulations. Figure 5 shows the separation of a mixture of three fluoresceintagged amino acids plus residual fluorescein; here, a sample plug was injected simultaneously into each of the five separation channels, and the separated peaks from all channels converged to a single channel and single detection area (Figure 1B). The top trace in Figure 5 shows the raw overlapping peaks detected as they exited the separation channels into the detection point. The measured data are shown as boxes overlaid on a simulated best-fit function. This first fit was made to illustrate the origin of the electropherogram and to act as a benchmark for the FT basisvector fit. To generate this first fit, we employed a time-domain fitting routine that is different from the basis-vector optimization routine described above. Because we knew that we should expect four analytes and because we knew their approximate mobilities from the single-channel separation on the chip, we were able to Analytical Chemistry, Vol. 79, No. 17, September 1, 2007

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Figure 6. Electropherogram after Fourier transform and the accompanying data processing. This electropherogram was obtained using the raw separation data shown in Figure 5. The single-channel separation was shown in the inset, which was obtained from the same chip but in a subsequent separation. Squares represent the coefficients of the basis vectors, and the solid line is the best-fit Gaussian curve.

employ a simplified, parametric fit. We used Mathematica’s FindFit routine to determine optimal values to enter into a model function of eight variables. The variables for this function are the mobility and concentration of each of four analytes, and the output is a simulated 20-peak simulation from 5 simulated channels. After determining optimal values for these variables, we used the values for the concentration and mobility of each individual component of the mixture to generate a simulated peak system that corresponds to each analyte. We show these individual simulations below the experimental data to help visually interpret the origins of the series of highly overlapping peaks. If we relate these extracted parameters to retention times from a single channel with length of 2.24 cm under an applied voltage of 1 kV, this parametric fit yields retention times of 85.6, 81.2, 67.2, and 52.0 s, which correlates with the actual retention times from the 2.24-cm channel (see inset in Figure 6). We used these extracted retention times to confirm the result of the basis-vector optimization routine applied to the same data, which is discussed below. Basis-Vector Optimization Routine for Analyzing FTCE Separation Data. To interpret the DFT of the data obtained from the experimental FTCE separation, we performed a basis-vector optimization routine as described for our simulations above. The basis vectors were derived from 600 simulated, 5-channel, singleanalyte separations with uniform concentrations, but which differed in terms of their simulated mobility. The range of simulated mobilities encompassed the mobilities of the analytes in the system (as calculated from the retention time of the first and last 6814

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peaks). This analysis is distinct from the parametric fit above in that the former relies on user input to determine the number of analytes in the system and thus the number of parameters to fit. In contrast, fitting an appropriate set of basis vectors will find an arbitrary number of analytes that fit the data. As with the simulated data in Figure 4, the basis-vector optimization routine fits a linear combination of the DFT of the basis vectors to the DFT of the real data shown in Figure 5. Because the relevant frequencies in the data set are limited to a rather narrow range at the low end of the frequency domain, we compared only elements 2-60 of the real component of the DFT data. The elements of the coefficient vector correspond to the factor by which each basis vector is multiplied to yield a minimum in the absolute difference between the combined basis vectors and the data. Figure 6 shows the result. For convenience of interpretation, the mobility of each basis vector is converted to the equivalent retention time in a 2.24-cm channel. The resulting calculated retention times are 52.0 ( 0.1, 67.1 ( 0.2, 81.3 ( 0.3, and 90.6 ( 0.1 (error based on the width of the Gaussian fit to each peak). These data agree well with the parametric fit with an average error of 1.4%. The actual peak size is better reflected in the maximal intensity rather than in the area in the FT fit. The integrated peak areas from the single-channel data are 1178, 4054, 3053, 2392, and the peak heights from the FT fit are 6.15, 26.1, 13.8, 5.7; after scaling, this gives agreement to within 35%. Using areas rather than peak heights from the FT fit resulted in 58% error. As such, this fitting system as reported should not be used for quantitative measurement of peak size.

Compared to the actual data collected at the exit of the 2.24cm separation channel, there is some discrepancy. The results of the FT analysis (Figure 6) and the standard CE separation (shown as an inset in Figure 6) are not perfectly reconcilable in terms of retention times. Both sets of data were taken from the same chip but on sequential runs. The discrepancy illustrates the irreproducibility of PDMS CE microchips from run to run. Nonetheless, the single-channel data also serve to show the increase in resolution of the system. Applying the same fitting strategy with the appropriate basis vectors to the single-channel data (i.e., with neither Fourier transform nor signal averaging of any kind) produced slightly less than 20% gain in S/N and resolution, which indicates that some noise was filtered out by representing the experimental data as a relative goodness-of-fit of various noiseless simulations. After processing using an equivalent basis-vector optimization routine, the separation using a single channel has a theoretical plate height of 9.8 × 10-5 cm while the multichannel data after FT indicates a height of 3.2 × 10-6 cm, which corresponds to an improvement of ∼30 times. The increase in S/N is from 16 in the single-channel case to 46 in the FT processed 5-channel case. This gain can be attributed to three sources: (1) from the fitting routine, (2) from the filtering of highfrequency noise in the FT based fit, and (3) from signal averaging of the combination of data from five channels. Therefore, the increase by a factor of 2.9 is beyond what would be expected from signal averaging alone (a factor of 2.2) due to these additional filtering effects. CONCLUSIONS The Fourier transform is well-known and broadly applied in spectroscopy and spectrometry, but applications to chemical separations remain limited. We demonstrated here FTCE using a PDMS chip and LIF detection, but in principle, this technique can be applied to a number of other modes of separation, such as capillary gel electrophoresis, and other modes of detection, such as electrochemical detection. The main advantages of this FTCE technique over conventional separation are improved sensitivity and resolution. The disadvantages are the additional computational complexity and the fact that the output of the separation cannot be collected easily for further sample purification. The latter disadvantage is moderated by the fact that sample collection is less common for CE than for other modes of separation, particularly on-chip where the sample size is very small. With regard to computational complexity and data fitting, our FT (25) He, M.; Jason, S. K.; Daniel, T. C. Appl. Phys. Lett. 2005, 87, 031916. (26) Edgar, J. S.; Pabbati, C. P.; Lorenz, R. M.; He, M.; Fiorini, G. S.; Chiu, D. T. Anal. Chem. 2006, 78, 6948-6954. (27) He, M.; Sun, C.; Chiu, D. T. Anal. Chem. 2004, 76, 1222-1227. (28) Rodriguez, I.; Spicar-Mihalic, P.; Kuyper, C. L.; Fiorini, G. S.; Chiu, D. T. Anal. Chim. Acta 2003, 496, 205-215. (29) Fiorini, G. S.; Chiu, D. T. BioTechniques 2005, 38, 429-446.

approach has lower computational requirements for increased numbers of channels in comparison to fitting in the time domain. So long as the waveform described by the peak system is well described in the time domain (i.e., peaks are represented by more than two data points), we can safely discard frequencies above the Nyquest limit and, thus, get a twofold reduction in the size of the basis vectors. In most cases, a considerably larger fraction of frequencies can be discarded, depending on the speed of the fastest analyte in the system. It is also important to note that taking the FT of sequences of peaks that do not completely fill the domain of interest effectively convolutes a step function with the data as compared with a continuous system of periodic peaks. This issue is accommodated implicitly by choosing appropriate basis vectors for the fitting routines employed here. Nonetheless, using a number of channels sufficiently large to generate a reasonable range of data containing continuous peaks from all analytes would make analysis of the FT domain data simpler still. Areas where this technique could be useful are where sample is plentiful (relative to the needs of chip-based analysis) and dilute (relative to the limit of the detection of a given detection method). Examples might include a droplet with a volume greater than a single sample plug.25,26 Rather than attempt sample concentration27 or a difficult alteration to the instrument, this technique makes efficient use of the sample that would otherwise be wasted. This technique also represents a method of improving the performance of an existing PDMS-based separation platform without resorting to more difficult fabrication techniques such as etched glass28 or other plastic chips.29 The injection scheme described here is simple to implement, takes advantage of the design flexibility offered by chip-based system, and may find use in other applications where parallel injections are desirable. ACKNOWLEDGMENT P.B.A. thanks the NSF for their support through the graduate research fellowship. B.R.D. thanks the Mary Gates foundation for an undergraduate research grant. P.B.A. also thanks David Dorsey for time spent on fabrication and preliminary experiments and Bryant Fujimoto for helpful discussion about Fourier Transform, deconvolution, and data fitting. This work was supported by the Keck foundation and by the National Institute of Health (EB 005179). SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review May 16, 2007. Accepted June 29, 2007. AC0710026

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