Anal. Chem. 1999, 71, 2130-2138
Shah Convolution Fourier Transform Detection H. John Crabtree,† Martin U. Kopp,‡ and Andreas Manz*
Zeneca/SmithKline Beecham Centre for Analytical Science, Department of Chemistry, Imperial College of Science, Technology and Medicine, London, SW7 2AY, U.K.
A new convolution-detection method was developed which converts multiple-point (Shah function) detection, timedomain electropherograms into frequency-domain plots by means of a Fourier transformation, allowing the analytes’ speeds to be viewed in terms of their “blinking” frequency; we have named this method Shah convolution Fourier transform detection, or SCOFT. This paper represents proof of principle of the detection concept. A micromachined glass stucture with a patterned layer of Cr on its top surface to form regularly spaced detection slits was used to perform capillary electrophoresis separations with 55-point, laser-induced fluorescence detection over 3.78 cm of the 6.6 cm separation channel. While this method can be easily integrated into a miniaturized total analysis system (µ-TAS), the principle is equally applicable to detection in full-sized analytical instrumentation. Single-component samples (fluorescein) migrating through the separation channel yielded a single peak in the frequency domain, and two-component samples (fluorescein and fluorescein isothiocyanate) yielded two resolved peaks, each at the expected frequency; harmonics were also observed. Advantages were seen in terms of isolation of the analyte peaks from interference such as baseline drift and line noise. Resolution is somewhat inferior to that seen in single-point detection, but it is thought that improved chip design and mathematical and instrument optimization will lead to performance superior to that of single-point detection. Detection systems in separation science are fairly diverse. Spectrochemical methods, such as absorbance, fluorescence, and chemiluminescence, are very popular; other common methods include those based on refractive index, thermal conductivity, electrical conductivity, electrochemistry, radiochemistry, and mass spectrometry. Of course, in these general categories many subcategories and variations also exist. Different methods have particular strengths such as nearly universal applicability, sensitivity, speed, low cost, information content, and instrumental simplicity. Virtually all of these methods are employed for single-point detection at or near the end of the column. The separation mechanism or mechanisms relevant to the particular separation method operate over a period of time and length of column such † Current address: Alberta Microelectronic Corp., 318-11315 87th Ave., Edmonton, Alberta T6G 2T9, Canada. ‡ Current address: Roche Diagnostics, Instrument Centre, Tegimenta AG, 6343 Rotkreuz, Switzerland.
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that the injected sample is resolved into its constituent analytes; a detector interrogates the column flow at a fixed position based on the physical/chemical property of choice and yields an analytical signal which is recorded over the duration of the separation. The analytical output is thus a time-domain plot of the analytical signal, such as a chromatogram or electropherogram. In other words, the chromatogram or electropherogram is a convolution of the detection function, which is a δ function in this case, with the separation function. Prominent techniques which do not use single-point detection include radiochemical detection in DNA sequencing, 2-D gel electrophoresis, and thin-layer chromatography. Furthermore, absorbance or refractive index array detection has been used either for spatial imaging1 of a length of a capillary, yielding a concentration profile along that segment of column, or for multiplediscrete-point detection along a column length,2 which through signal averaging can improve S/N. Transformations and convolutions of traditional time-domain signal output have also been performed. Transferring the electropherogram data from the time domain to the reciprocal time domain was shown to be advantageous for evaluating analyte electrophoretic mobilities.3 Fourier transformations (FTs) have been applied to the separation time domain for self-optimizing Wiener data filtering,4 for correlating data from different lanes in gel electrophoresis separations of bacterial proteins,5 for data compression,6 and for deconvoluting peak smearing encountered with flow-radioactivity detectors for high-performance liquid chromatography,7 but only with the objective of regenerating or clarifying the time-domain information with minimal information loss. Cross-correlation between semicontinuous injection patterns and detector signal has been applied to capillary zone electrophoresis separations, yielding an approximate 8-fold enhancement in the signal-to-noise ratio.8 Of course, FTs have also been applied to the spectral time domain, such as in FT-MS, FT-NMR, and FT-IR spectrometers, and the last has been used for detection on a microchip,9 but while (1) Wu, J.; Pawliszyn, J. Anal. Chem. 1994, 66, 867-873. (2) Culbertson, C. T.; Jorgenson, J. W. Anal. Chem. 1998, 70, 2629-2638. (3) Mammen, M.; Colton, I. J.; Carbeck, J. D.; Bradley, R.; Whitesides, G. Anal. Chem. 1997, 69, 2165-2170. (4) Economou, A.; Fielden, P. R.; Packham, A. J. Anal. Biochem. 1996, 319, 3-12. (5) Millership, S.; Ragoonaden, K. Comput. Biomed. Res. 1992, 25, 392-406. (6) Cai, C.; Harrington, P. d. B. Anal. Chem. 1997, 69, 4249-4255. (7) Bonnot, G.; Febvay, G. Anal. Biochem. 1995, 224, 354-363. (8) van der Moolen, J. N.; Poppe, H.; Smit, H. C. Anal. Chem. 1997, 69, 42204225. (9) Lendl, B.; Schindler, R.; Frank, J.; Kellner, R.; Drott, J.; Laurell, T. Anal. Chem. 1997, 69, 2877-2881. 10.1021/ac981266f CCC: $18.00
© 1999 American Chemical Society Published on Web 04/28/1999
Figure 1. Shah convolution Fourier transform detection (SCOFT) principle. The concept is easily visualized for a single-component sample and laser-induced fluorescence. (A) Experimentally, a sample plug is injected into the separation column, which is masked from the excitation light except at transparent detection slits. When the plug reaches a slit (as at t2 and t4), its fluorescence reaches the detector; otherwise, no light reaches the detector (t1, t3). (B) The detector signal shows regularly spaced peaks along the time axis; when the data are transformed, a single frequency peak results. An injection of several analytes would produce several frequency peaks, one per analyte.
this adds a new information dimension (mass, nuclear magnetic resonance, or infrared absorption) if used for the detection of a separation, the analytical signal remains in the time domain. We propose a new detection system comprising a new method of column interrogation and a corresponding domain for analytical separation data presentation based on a convolution of the detection function similar to the Shah function, followed by Fourier transformation. Therefore, we propose to name it Shah convolution Fourier transform detection, or SCOFT. Briefly, a Shah function, III(x), is an infinite sequence of unit impulses, δ(x), spaced at unit intervals: ∞
III(x) )
∑
δ(x - n)
(1)
n)-∞
In this approach, the separation is constantly interrogated at a number of evenly spaced points along the column simultaneously by a single detector, such that signals measured from all of these points along the column are summed. Thus, during the separation, each analyte band or zone progressing along the column at its characteristic speed will produce a series of evenly spaced Gaussian peaks, and the chromatogram or electropherogram will be the resultant sum of these several series of Gaussian peaks, n series for n analytes. This represents the time-domain electropherogram signal: Shah convolution of point detection. A Fourier
transformation in the forward direction transforms a time-domain signal to the frequency domain and will thus show the frequency components which comprise the time-domain signal. Upon application of a Fourier transformation to the time-domain electropherogram, a frequency-domain plot is produced in which each individual series of Gaussian peaks (from the time domain) produces its characteristic frequency peak. While this detection principle is applicable to a variety of separation-detection scenarios, we feel it can most easily be explored on a miniaturized total analysis system (µ-TAS) device10 designed for electrophoretic separations and laser-inducedfluorescence (LIF) detection. The concept, as applied to our microstructure and LIF system, is depicted in Figure 1. Microfabrication has obvious advantages in the ease with which the separation channels and detection slits in such a device can be fabricated and in their alignment to each other. µ-TAS is the field of analytical chemistry which seeks to reproduce existing methods as well as create new methods of chemical analysis on the micrometer scale on centimeter-sized chips made of glass, silicon, or polymeric materials. These miniaturized, integrated systems offer either real or expected benefits in terms of analytical figures of merit such as separation time and plate count and in terms of portability and automation (10) Manz, A.; Graber, N.; Widmer, H. M. Sens. Actuators, B 1990, 1, 244-248.
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Figure 2. Instrumental apparatus. An Ar+ laser beam is expanded, converged to parallel, and focused onto the separation channel of the electrophoresis chip by cylindrical lenses. Fluorescence produced at the detection slits of the chip when a sample passes beneath is filtered from the excitation light and then transduced with a photomultiplier tube.
as well as reagent and instrumentation cost;11 real challenges for detection arise, however, from the small volumes and path lengths involved. A good explanation and review of the field were presented a few years ago,12 while the latest developments are gathered in a recent conference proceedings publication.13 It is thought that there may be advantages to be reaped from SCOFT in terms of signal-to-noise ratios and resolution with regard to conventional single-point detection, given the repeated sampling of the separation, and in terms of immunity to baseline drift and environmental noise, given their frequency dependence. The existence or magnitude of these advantages may, however, be very dependent upon experimental conditions. EXPERIMENTAL SECTION Apparatus. A box diagram of the instrumentation is given in Figure 2. The lenses, laser, chip, and electrodes were mounted with lens mounts or custom-made fixtures on carriers along a vertically mounted 2 m optical rail (lens mounts and posts on an X-95 rail and carrier system, Newport, Irvine, CA); the photomultiplier tube (PMT) was mounted in a ring stand. The whole apparatus was enclosed in a light-tight galvanized steel box. A 50 mW multiline Ar+ laser (lines at 457, 465, 472, 477, 488, and 496 nm; model 532-B-A01, OmNichrome (Melles Griot), Chino, CA) running in standby mode (∼11 mW) was shone initially upon two concave cylindrical lenses (01LCN000, f ) -6.35 mm; Melles Griot, Cambridge, U.K.) spaced 7 mm apart, to expand the beam, and then upon a convex cylindrical lens (01LCP013, f ) 150 mm; Melles Griot) 14 cm from the nearest concave lens above, producing a parallel beam expanded along one dimension to 4.5 cm (limited by the convex lens and holder) to cover the length of the separation channel. The beam then passed through a second convex cylindrical lens (01LCP009, f ) 80 mm; Melles Griot) with its cylindrical axis rotated 90° around the beam axis with respect to the previous lenses. This lens acted to focus the (11) Kopp, M. U.; Crabtree, H. J.; Manz, A. Curr. Opin. Chem. Biol. 1997, 1, 410-419. (12) Manz, A.; Harrison, D. J.; Verpoorte, E.; Widmer, H. M. Adv. Chromatogr. 1993, 33, 1. (13) Harrison, D. J., van den Berg, A., Eds. MicroTotal Analysis Systems 98; Conference Proceedings for µ-TAS ‘98, Oct 13-16, 1998, Banff, Canada; Kluwer Academic Publishers: Dordrecht, 1998; 492 pp.
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Figure 3. Micromachined glass electrophoresis chip: (A) schematic showing the solution reservoirs, electrophoresis channels, and patterned Cr layer for the layout used; (B) scanned image of the actual 75 mm × 75 mm chip. The six different channel systems can be seen; the components of the channel system used are highlighted.
beam onto the width of the channel. While beam focus was 8.0 cm beneath this lens, the chip was purposely positioned 9.3 cm beneath the lens to illuminate the full width of the channel. The chip was held in the apparatus with a locally built holder which fixes the chip in the optical path and the Pt electrodes in the reservoirs and provides high-voltage contacts for the electrodes. The micromachined electrophoresis chips were manufactured at the Alberta Microelectronic Corp. (Edmonton, Canada) on Corning no. 0211 glass substrates (Corning, NY). All channels were ∼15 µm deep, 50 µm wide at the top and 20 µm wide at the bottom. The 0.5 mm thick cover plate was thermally bonded to the substrate and had 2 mm diameter holes drilled through for sample and reagent reservoirs. A ∼1000 Å Cr layer was plated and patterned on the top side of the cover plate to provide the detection slits. The 55 slits were each 300 µm wide and were spaced 700 µm center to center. The chip contained six separate designs, but only the one used in the present work will be described in detail. The layout, illustrated in Figure 3, was a simple cross pattern of two intersecting channels and four reservoirs: (a) the sample injection channel with sample and sample waste reservoirs, and (b) the separation channel with buffer and buffer waste reservoirs, above which the detection slits lay. Reservoirs consisted of ∼5 mm sections of micropipet tips epoxied to the glass surface around the 2 mm drilled holes, providing a reservoir volume of ∼50 µL each. Channel lengths, measured from the intersection, were 3.62 cm to the sample reservoir, 3.92 cm to the buffer reservoir, 4.86 cm to the sample waste, and 6.60 cm to the buffer waste.
Detection was performed with a 2 in. head-on PMT (R550 PMT, E1198-11 socket, C3830 power supply, Hamamatsu Photonics, Middlesex, U.K.) with three high-pass interference filters (505EFLP, Omega Optical, Brattleboro, VT), three high-pass Schott filters (OG515, Edmund Scientific, Barrington, NJ), and one fluorescein emission band-pass filter (520DF15, Omega Optical) attached to the PMT, the last next to the PMT. The filter edges and PMT-filter interface were carefully foil-wrapped to eliminate unfiltered light from reaching the PMT. The PMTfilter assembly was mounted 5.3 cm from the center of the separation channel, at an angle of 28° from the plane of the laser beam. Current signal from the PMT biased at -1000 V was summed with an adjustable user-defined “baseline-shift” current, amplified with a current follower (Rf ) 33 MΩ), filtered with a single-stage active low-pass filter (194 Hz nominal cutoff frequency), and then acquired at 100 Hz (buffered) on an Apple Power MacIntosh 9500/ 120 through a 16-bit data acquisition board (PCI-MIO-16XE-50, National Instruments, Berkshire, U.K.) with a program written in LabView 5.0 (National Instruments). Data manipulation and fast Fourier transforms (FFTs) were performed on Igor Pro 3 (Wavemetrics, Lake Oswego, OR) with Microsoft Excel 5.0 after acquisition. Potentials at the four electrodes were controlled by a homemade power supply, wherein discrete 3 kV dc-dc converters (one per electrode) were regulated via multiplexing from another LabView program running on a Viglen P5/133 PC. This allowed effective switching of all four electrodes in about 300 ms and current sourcing or sinking at any electrode, as well as independent current and voltage monitoring. Reagents and Solutions. Tris-borate-EDTA (TBE) buffer was first prepared at 5× concentration (445 mM in both tris(methoxy)aminomethane and boric acid, 10 mM in ethylenediaminetetraacetic acid; prepared from a solid TBE mixture, Fluka), then diluted with deionized water (water purification system, Elga Ltd., Bucks, U.K.) to 1× and 0.1× concentrations, and finally filtered through 0.45 or 0.2 µm filters. Stock solutions of 2.54 mM fluorescein (free acid, Fluka) in 1× TBE and of 50 mM fluorescein isothiocyanate (FITC) (isomer I, Fluka) in acetone (BDH) were prepared with sonication. Appropriate amounts of each stock solution were diluted with deionized water and/or 0.1× TBE to make both a 254 µM fluorescein in 0.1× TBE solution and a 64 µM fluorescein, 125 µM FITC in 0.1× TBE solution. Cleaning solutions of 1.4 M HNO3 and 1.0 M NaOH were prepared from deionized water, concentrated nitric acid (65% (w), Fluka), and sodium hydroxide (BDH). Preparatory and Experimental Procedure. To prepare the chip, cleaning fluids were drawn into the chip by applying vacuum to one reservoir and supplying the other three with the appropriate fluid; for a given fluid rinse, vacuum, supplied by a 50 mL syringe, was applied to all four reservoirs in turn, 4 min each. Daily chip preparation consisted of drawing through first 1.4 M HNO3, then 1.0 M NaOH, and finally the running buffer, 0.1× TBE. The sample solution was then loaded into the sample reservoir, and the chip was ready to run. For overnight storage, the chip was filled with water and reservoirs were sealed with Parafilm. Prior to experiments on the apparatus described above, the four-step high-voltage protocol used for chip alignment and
Table 1. Typical High-Voltage Program Used To Align the Chip and Inject and Separate a Sample reservoir potential (V) step
sample
buffer
sample waste
buffer waste
time (s)
sample fill purge injection plug separation
3000 1800 3000 1800
2000 3000 2000 3000
2000 1800 0 1800
0 0 2000 0
60 60 10 60
electrophoresis was evaluated by being performed on the chip under an inverted microscope (Leica DMIL equipped with a fluorescein filter cube and halogen lamp, Leica, Milton Keynes, U.K.). This prerun evaluation ensured that the sample plug was properly formed at and injected from the channel intersection and that no sample leakage occurred during the length of the run. Once an injection-separation protocol had been executed correctly under the microscope numerous times, the chip’s separation channel was filled with a fluorescent sample (step 1) and immediately transferred to the detection apparatus. The chip was then aligned to the expanded laser beam with translation stages, the box was closed and sealed, and, following a purge of the separation channel of the fluorescent aligning solution (step 2), the injection plug formation (step 3) and separation (step 4) protocol was run while the electropherogram was recorded. A typical voltage protocol is shown in Table 1. For the drifting-baseline injections, a slightly different voltage protocol was used. First, an injection of fluorescein with intentional leakage of sample into the separation channel was performed, with high voltages at the sample and sample waste reservoirs during the separation step, to simulate a gradual increase in the background signal. Second, a normal injection was performed, with lower voltages at the sample and sample waste reservoirs, such that no sample leakage occurred. For the two-component injection, the fluorescein and FITC solution was injected with different “pinching” voltages at the buffer and buffer waste reservoirs in the injection plug formation step: runs 1-5 were as shown in Table 1, with 2000 V, runs 6 and 7 had 2250 V applied, and runs 8 and 9 had 1900 V applied. The effect of increasing the pinching voltages at the buffer and buffer waste reservoirs as their solutions and the sample solution flow to the sample waste reservoir is to increase the buffer:sample flow ratio, which in turn reduces the sample plug size at the channel intersection. To achieve point detection in runs 1-3, two pieces of aluminum foil were taped over all of the slits save the 49th; the apparatus was otherwise identical. After these three runs, the foil was removed, exposing all 55 slits, and runs 4-9 were performed. Data were acquired and stored as text files in LabView and processed in Igor. The postdetector electronics (current follower and low-pass filter) yielded a negative signal, so data were digitally inverted to produce positive peaks. Time ) 0 for the electropherogram was selected as the beginning of the separation step in Table 1, and data for an even number of points bracketing the relevant time span (the 3500-point segments of Figures 4A, 6A, and 7B and the 5000-point segments of Figure 5A) were then treated with an FFT in the forward direction to yield the frequency-domain data. No apodization or zero-padding was performed on the timeAnalytical Chemistry, Vol. 71, No. 11, June 1, 1999
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Figure 4. One-component injection. (A) Time-domain data produced when a fluorescein sample is injected down the separation channel: 55 peaks, spaced at 0.58 s, superimposed on the Gaussian distribution of the expanded laser beam. (B) Fourier transformation of part A, displayed in magnitude formats: peaks for 1.74 Hz (∼1/0.58 s) fundamental and 3.43 Hz harmonic can be seen.
domain data (Igor is capable of Fourier transforming any even number of points). The FFT algorithm yields (N/2) + 1 complex points (pairs of real and imaginary points) in the frequency domain for an input of N real points in the time domain. For real input, only the positive side of the frequency spectrum is generated by the FFT, since the positive and negative frequency spectra are identical. These complex data can also be represented in terms of their magnitude (Figure 4B):
FTνi,Mag ) (FTνi,Re2 + FTνi,Im2)1/2
(2)
It is easier to visualize the magnitude of the frequency response, especially for two (or more)-component separations, so data are presented in this form throughout. RESULTS AND DISCUSSION One-Component Injection. A simple injection of fluorescein provides a good illustration of how the instrument functions; the 254 µM fluorescein in 0.1× TBE solution was used for a sample, with 0.1× TBE as running buffer. The electropherogram, beginning from when the sample plug was injected from the cross, is shown in Figure 4A; the data have been smoothed with a second order, Savitzky-Golay 25-point algorithm.14,15 Fifty-five peaks can (14) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627-1639. (15) Igor Pro 3 Programming and Reference Manual, 3rd ed.; WaveMetrics: Lake Oswego, OR, 1996.
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be seen to occur in ∼35 s, one every 0.58 s. After the 55th peak, the trace returns to the baseline level since the sample plug has migrated to a section of the capillary beneath the Cr mask. In Figure 4B, the Fourier transformation of the signal trace of Figure 4A can be seen. The average spacing of the peaks in the time domain is 0.58 s, so a frequency peak would be expected at 1/(0.58 s) ) 1.7 Hz; indeed, one is seen at 1.74 Hz, but one is also seen at 3.43 Hz. The latter peak represents the first harmonic frequency, and the second harmonic has been observed in other experimental data as well; this is an expected if unfortunate byproduct of the FT, which will give rise to interference in multicomponent analysis if migration velocities differ by a factor of 2 or greater. The Fourier transformation is sinusoidally based and, given a sine wave input in the time domain, generates a δ function at the fundamental frequency in the transformation; however, given a series of Gaussian waveforms, the Fourier transformation shows decreasingly intense peaks at increasing harmonic frequencies, in addition to the strong fundamental frequency peak. A simple demonstration of this phenomenon was performed beforehand, by mathematically generating a data set with one or two series of Gaussian peaks for one or two analytes and witnessing the occurrence of the strong fundamental and weaker harmonics in the FFT of the set. The harmonics observed were of greater order and higher amplitude in the simulated data than in real data; we have no explanation for this observation at present, although we note that the simulated data set did not have any noise on the signal, nor
Figure 5. Baseline drift. (A) Electropherograms of a regular fluorescein injection and one with intentional baseline drift caused by sample leakage into the separation channel after injection. (B) Fourier transforms of part A: the baseline drift manifests itself as the broad peak beneath ∼1 Hz; analyte peaks are essentially segregated from the drift in the frequency domain.
was the Gaussian excitation profile, described next, accounted for. A reviewer has also pointed out that it should be possible to model and predict the presence of harmonic peaks and therefore filter them out. Another striking feature in the time-domain data is an apparent gradual baseline drift which reaches a maximum at about peak 20 or 25 and disappears by the end of the run. This “drift” is present in all electropherograms and likely reflects the Gaussian intensity profile of the expanded laser beam; the analyte passes through excitation radiation of varying intensity, and so its fluorescence varies accordingly. This is supported by laser power meter readings at various distances along the expanded beam (data not shown). The effect contributes to the low-frequency, broad peak below about 0.2 Hz in the frequency domain. This frequency-domain isolation of low-frequency drift from the superimposed signal in the time domain would seem an apparent advantage of this technique. An experiment was performed in which injections were made both normally and with dilute sample leaking into the separation channel after the sample plug was injected, to simulate gradually increasing background signal, or baseline drift. The results are shown in Figure 5; the time-domain plot, Figure 5A, shows two traces, one for a normal injection, similar to Figure 4, and one for an injection with leakage, in which the peaks are superimposed on an upward-sloping baseline. The frequency-domain plots for these data are shown in Figure 5B. The drifting baseline manifests itself in the frequency domain as a much broader, low-frequency peak, as seen in
comparison to the trace for the normal injection. The analyte peak is essentially isolated from the drift. A shoulder peak on the fluorescein peaks in the frequency domain, as well as a shift in the frequency, is noticeable in Figure 5. The shoulder peak may be due to somewhat uneven fluorescein leakage after the sample plug injection. The frequency shift in Figure 5B is due to a change in the electroosmotic velocity and is not related to the detection method, as shown by the corresponding change in the time-domain peak spacing of Figure 5A. Similarly, frequency-domain isolation of high-frequency noise from analyte peaks is observed. Line noise at 50 Hz is present in all the electropherograms recorded and produces a peak at 50 Hz in the frequency-domain plots (50 Hz is also the Nyquist limit, given the 100 Hz data acquisition used). If the electropherograms are smoothed with a second-order, Savitzky-Golay 25-point smoothing algorithm, a substantial improvement in signal-to-noise ratios is seen in the time domain, but in the frequency domain, the 50 Hz peak merely disappears; analyte peaks are unaffected. This is documented by the results given in Figure 6. The advantage of segregating baseline drift, line noise, and other frequency-specific interference from analyte peaks in SCOFT will depend on the frequency range the analyte peaks fall into, as well as the rate of baseline drift. The analyte frequencies depend on their electrophoretic mobilities and the electroosmotic mobility (and thus on their charge-to-size ratios, the applied electric field, buffer composition, and chip substrate composition), as well as on detection slit spacing on the chip. Taking the baseline drift Analytical Chemistry, Vol. 71, No. 11, June 1, 1999
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Figure 6. Line noise. (A) Smoothed (second-order, Savitzky-Golay 25 point) time-domain data from Figure 4A have enhanced S/N compared to raw data. (B) In frequency-domain data, analyte peaks are already segregated from line noise, so smoothing is not needed. (C) Time-domain smoothing merely reduces the peaks at 50 Hz. Table 2. Single-Point-Detection Migration Time Data for Two-Component Injections from Figure 7A, with Corresponding Calculated Migration Speeds and Migration Fluorescence “Blinking” Frequencies
analyte FITC fluorescein
time, tmig (s) run 1 run 2 run 3
avg
25.9 27.1
26.1 27.3
26.4 27.6
26.1 27.3
Table 3. Experimental Frequency-Domain Maxima Corresponding to the Blinking Frequencies of FITC and Fluorescein for Six Injections Shown in Figure 7C freq (Hz)
freq (Hz)
freq,b
νmig,fl (Hz)
run no.
FITC
fluorescein
run no.
FITC
fluorescein
vmig (mm/s) 1.32 1.26
1.89 1.81
4 5 6
1.94 1.94 1.91
1.86 1.86 1.83
7 8 9
1.91 1.91 1.89
1.83 1.83 1.80
velocity,a
a Migration velocity is calculated as v mig ) 34.5 mm/tmig,avg, where 34.5 mm is the distance from injection to the 49th slit. b Migration fluorescence frequency is calculated as νmig,fl ) vmig/0.7 mm, where 0.7 mm is the center-to-center slit spacing.
case above as being fairly severe, the current design affords a fairly broad analyte frequency window which is line-noise and drift free, ∼1-48 Hz, regardless of these interferences in the time domain. Two-Component Injection. The results of the fluorescein and FITC sample injections can be seen in Figure 7. The first three runs had single-point detection and were designed to show a normal electropherogram of the separation of the two species, as well as to allow the beat frequency in the time domain and frequencies and approximate magnitudes of the peaks in the frequency domain to be predicted. These runs are shown in Figure 7A. The migration times, velocities, and expected frequencies for migration fluorescence for the fluorescein and FITC peaks are shown in Table 2. Imprecision in the migration times arises from the fact that the operator must at present synchronize a stopwatch with the beginning of the voltage program. The runs which followed (4-9) were repeats of the sample injection, but with all 55 slits exposed and with different injected plug sizes. Injection quantities were not measured, but by virtue of the pinching voltages described in the Experimental Section, runs 4 and 5 would be expected to have the same quantity injected as in runs 1-3, runs 6 and 7 slightly less, and runs 8 and 9 slightly more. The electropherograms generated are shown in Figure 7B. Apart from the facts that the signal is made from two series of 2136 Analytical Chemistry, Vol. 71, No. 11, June 1, 1999
unipolar Gaussian waveforms (not two bipolar sinusoidal waveforms) and that the ∼55 peaks are again superimposed upon the broad Gaussian laser beam distribution, each electropherogram is in essence an interferogram of two frequencies; a beat pattern in the data arising from this interference is evident. Given the two frequencies calculated in Table 2, we would predict a beat period similar to that observed. If vFluor and vFITC are the migration velocities from Table 2, dspacing is the center-tocenter slit spacing (0.7 mm), and TBeat is the beat period, defined as the time required for the peaks to become separated by dspacing, then we can write
TBeat(vFITC - vFluor) ) dspacing
(3)
TBeat is thus determined to be 11.7s, in fair agreement with the 11.5 s observed in the plots of Figure 7B. When the time-domain electropherograms of Figure 7B are transformed, the frequency-domain plots of Figure 7C are generated. Two clear peaks at about 1.8 and 1.9 Hz can be seen in each case, along with their first harmonic peaks at 3.6 and 3.8 Hz. The fundamental frequencies are listed in Table 3 and are close to the values predicted in Table 2. One may also note a slow drifting of the frequencies to lower values from one run to the next; this likely reflects a reduction in electroosmotic flow over the course of the experiment (∼1.5 h). While it is clear that there are two frequency components, the resolution is not as good as that for the single-point detection
Figure 7. Two-component injection. (A) Single-point detection electropherograms of a fluorescein and FITC sample show two baselineresolved peaks; data can be used to predict beat period and frequencies (see text). (B) 55-point electropherograms generated for six injections: an interference pattern from the two species is obvious. (C) Fourier transformations of the electropherograms of part B: two fundamental frequencies at ∼1.8 Hz are obvious, but harmonics at ∼3.7 Hz are also visible.
electropherograms shown in Figure 7A, which achieve baseline resolution of the two components. The separation resolution in the frequency domain can be increased by lengthening the interference pattern, such that more beats are present in the timedomain data. Instrumentally, this amounts to increasing the number of detection slits, which is analogous to increasing the mirror displacement in a Michaelson interferometer in a Fourier transform infrared spectrometer, for example. A different design could have the detection slits closer together, to achieve faster
resolution, but the practical limitation of band broadening would soon be encountered, wherein a diffuse analyte zone toward the end of the separation might span two or more slits if they were spaced too closely. Having a single zone span two or more slits in the current design would in essence decrease the signal-tobackground level: instead of emission at one slit (signal) contrasted to no emission (background), which is the case for the data shown in this paper, one would have emission at two slits contrasted to emission at one slit, that at three slits contrasted Analytical Chemistry, Vol. 71, No. 11, June 1, 1999
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to that at two slits, etc. If sensitivity were abundant, it might be possible to sacrifice sensitivity for resolution, by creating a finedetection slit pattern, with each zone spanning several slits but resulting in a much longer interference pattern in the data produced over the same channel length. In addition, with any slit pattern, two factors which will affect peak width in the frequency domain and hence resolution are inhomogeneities in an analyte’s migration speed along the channel and imperfections in the slit spacing. Signal-to-noise ratios observed in any of the time-domain PMT traces are not very high, considering the concentrations of solutions injected. This is because, thus far, efforts have been focused on demonstrating the principles of the detection concept and not on optimizing the optics and electronics of the detection system. CONCLUSIONS In this article we have demonstrated proof of principle for Shah convolution Fourier transform detection. With appropriate signal convolution in the time domain, one- and two-component samples yield one and two peaks, respectively, in the frequency domain, and the peaks generated are at the correct frequencies. Further, advantages with respect to isolation of the analytical signal from baseline drift and line noise are realized with this method by virtue of their frequency dependencies. Resolution obtained in the frequency domain for the two-component separation was inferior
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to that seen in the time domain with single-point detection; sensitivity has not yet been investigated. The scope for future investigations into SCOFT is quite wide. To begin with, both a comparison of single-point detection with SCOFT and a resolution enhancement by increasing the number of detection slits seem obvious. Applying SCOFT to different detection methods based on absorbance, electrochemistry, electrochemiluminescence, and refraction index would be of interest. Further, different convolution patterns and/or mathematical transformations could be applied to the separation time domain, possibly yielding better and faster resolution and possibly eliminating overtones. ACKNOWLEDGMENT Financial support from SmithKline Beecham and Zeneca, as well as from the BBSRC and EPSRC (ROPA), is gratefully acknowledged. We wish to thank the Alberta Microelectronic Corp. for fabricating the microstructures used in this study. H.J.C. also thanks Andrew de Mello, David Colling, Thomas von Schroeter, and David Thornley for insightful discussions and Yien C. Kwok for assistance with the figures.
Received for review November 17, 1998. Accepted March 16, 1999. AC981266F
