Anal. Chem. 1998, 70, 4463-4471
Fluorescence Correlation Spectroscopy for Rapid Multicomponent Analysis in a Capillary Electrophoresis System Alan Van Orden and Richard A. Keller*
Chemical Science and Technology Division, MS M888, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
We describe a new technique for performing multicomponent analysis using a combination of capillary electrophoresis (CE) and fluorescence correlation spectroscopy (FCS), which we refer to as CE/FCS. FCS is a highly sensitive and rapid optical technique that is often used to perform multicomponent analysis in static solutions based on the different diffusion times of the analyte species through the detection region of a tightly focused laser beam. In CE/FCS, transit times are measured for a mixture of analytes continuously flowing through a microcapillary in the presence of an electric field. Application of an electric field between the inlet and outlet of the capillary alters the transit times, depending on the magnitude and polarity of the applied field and the electrophoretic mobilities of the analytes. Multicomponent analysis is accomplished without the need to perform a chemical separation, due to the different electrophoretic mobilities of the analytes. This technique is particularly applicable to ultradilute solutions of analyte. We have used CE/FCS to analyze subnanomolar aqueous solutions containing mixtures of Rhodamine 6G (R6G) and R6Glabeled deoxycytosine triphosphate nucleotides. Under these conditions, fewer than two molecules were typically present in the detection region at a time. The relative concentrations of the analytes were determined with uncertainties of ∼10%. Like diffusional FCS, this technique is highly sensitive and rapid. Concentration detection limits are below 10-11 M, and analysis times are tens of seconds or less. However, CE/FCS does not require the diffusion coefficients of the analytes to be significantly different and can, therefore, be applied to multicomponent analysis of systems that would be difficult or impossible to study by diffusional FCS. There are many applications in analytical chemistry for rapid, ultrasensitive analytical techniques capable of measuring the contents of a multicomponent solution. Separation techniques such as capillary electrophoresis (CE) coupled to such ultrasensitive detection methods as laser-induced fluorescence (LIF) represent the current state of the art in terms of sensitivity and selectivity. However, with conventional CE, time scales of minutes to tens of minutes are required to achieve a complete separation. Methods capable of performing the analysis in tens of seconds or less would be of great value for many bioscience applications. 10.1021/ac980768q CCC: $15.00 Published on Web 10/07/1998
© 1998 American Chemical Society
Several groups have reported on electrophoresis detection methods capable of rapidly characterizing analytes by their electrophoretic mobilities without performing a chemical separation. As early as 1971, Ware and Flygare reported on a method to measure the electrophoretic mobilities of bovine serum albumin molecules from the Doppler shift of Rayleigh scattered laser light, measured using laser beat frequency spectroscopy.1 The authors showed that the measurement could be performed in tens of seconds to minutes and suggested extending the technique to rapid multicomponent analysis of macromolecules possessing different electrophoretic mobilities. Scattering techniques of this kind, however, have not been widely used as detection methods for CE because they are inherently less sensitive than other detection methods, like LIF, and are generally not applicable to smaller molecules. More recently, Chu and co-workers combined gel electrophoresis with the movements of fluorescence pattern after photobleaching (MOFPAP) technique to rapidly measure the electrophoretic mobilities of large DNA fragments in an agarose gel matrix.2-4 Analysis times of less than 10 min were reported, compared to several hours that are normally required for conventional gel and pulsed field gel electrophoresis. Finally, Castro and Shera described a single-molecule electrophoresis (SME) setup that was used to identify single analyte molecules in a CE system from their transit times between two focused laser beams.5 These authors showed that analysis times of seconds or less could be achieved for analyte concentrations as low as a few femtomolar. The SME technique requires that the analytes be detectable at the single-molecule level with high signal-tobackground ratios and is limited by diffusion of the analytes during their transit between the two laser beams. Therefore, the best discrimination between different analytes was achieved for mixtures of highly fluorescent, slowly diffusing species such as large DNA fragments labeled with intercalating dyes and proteins labeled with phycoerythrin. An alternative method for ultrasensitive multicomponent analysis is fluorescence correlation spectroscopy (FCS). FCS is a solution-phase optical technique that is used to monitor timedependent fluctuations in the fluorescence intensity from a small subvolume of the solution, defined by the near diffraction-limited focal region of an excitation laser beam. These fluorescence (1) (2) (3) (4) (5)
Ware, B. R.; Flygare, W. H. Chem. Phys. Lett. 1971, 12, 81-85. Wang, Z.; Chu, B. Phys. Rev. Lett. 1989, 63, 2528-2531. Wu, C.; Wang, Z.; Chu, B. Biopolymers 1990, 29, 491-500. Chu, B.; Wang, Z. L. Electrophoresis 1992, 13, 536-541. Castro, A.; Shera, E. B. Anal. Chem. 1995, 67, 3181-3186.
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intensity fluctuations are caused by alterations in the number of fluorescent molecules present in the detection volume due to such processes as diffusion, 6-9 uniform translation,10,11 photochemical transformations,12 chemical reactions,13-15 intermolecular dynamics,16 and conformational fluctuations.17 From autocorrelation analysis of the time-resolved fluorescence signal, one can obtain such information as absolute and relative concentrations, diffusion rates, flow rates, triplet-state lifetimes, and reaction rates of the analyte species. In recent years, the sensitivity of FCS has been improved considerably by combining this technique with confocal fluorescence microscopy, thus limiting the detection subvolume to a few femtoliters or less. The background luminescence intensity due to scattering of the excitation laser beam by the solvent molecules present in the detection volume is so small that fluorescence bursts from single molecules flowing through the detection volume can be detected above the background. This allows FCS measurements to be performed for analyte solution concentrations as low as ∼10-12 M in less than 1 min. Analysis times as low as a few seconds or less can be achieved by increasing the solution concentration, having the analyte solution flow, or rapidly scanning the detection region. FCS is most commonly used to measure diffusion rates of molecules in static solutions for such applications as the detection and characterization of probe-target binding.13-15 In these experiments, the extent of reaction is monitored by observing a decrease in the average diffusion rate of a fluorescent probe molecule upon binding to the target. One of the limitations of these assays is that the target molecule must be a much more slowly diffusing species than the probe in order to observe a large enough change in the diffusion rate to discriminate between bound and unbound probe molecules. There are many examples of probe-target binding assays in which the probe and the target molecules are comparable in size, as well as cases where the target is actually smaller than the probe. These types of assays are difficult or impossible to study by conventional FCS. Two FCS techniques have recently been described that can be applied to probe-target binding assays where the binding of the probe to the target does not significantly alter the diffusion rate of the probe. These are two-color fluorescence cross-correlation spectroscopy18,19 and scanning fluorescence correlation spectroscopy.20 (6) Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1-27. (7) Elson, E. L.; Magde, D.; Webb, W. W. Biopolymers 1974, 13, 29-61. (8) Rigler, R.; Widengren, J.; Mets, U ¨ . In Fluorescence Spectroscopy; Wolfbeis, O. S., Ed.; Springer-Verlag: Berlin, 1993; pp 13-24. (9) Rigler, R.; Mets, U ¨ .; Widengren, J.; Kask, P. Eur. Biophys. J. 1993, 22, 169-175. (10) Magde, D.; Webb, W. W.; Elson, E. L. Biopolymers 1978, 17, 361-376. (11) Brinkmeier, M.; Do¨rre, K.; Riebeseel, K.; Rigler, R. Biophys. Chem. 1997, 66, 229-239. (12) Widengren, J.; Mets, U ¨ .; Rigler, R. J. Phys. Chem. 1995, 99, 13368-13379. (13) Kinjo, M.; Rigler, R. Nucleic Acids Res. 1995, 23, 1795-1799. (14) Schwille, P.; Oehlenschla¨ger, F.; Walter, N. Biochemistry 1996, 35, 1018210193. (15) Rauer, B.; Neumann, E.; Widengren, J.; Rigler, R. Biophys. Chem. 1996, 58, 3-12. (16) Widengren, J.; Dapprich, J.; Rigler, R. Chem. Phys. 1997, 216, 417-426. (17) Wennmalm, S.; Edman, L.; Rigler, R. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 10641-10646. (18) Schwille, P.; Meyer-Almes, F.-J.; Rigler, R. Biophys. J. 1997, 72, 18781886. (19) Koltermann, A.; Kettling, U.; Bieschke, J.; Winkler, T.; Eigen, M. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 1421-1426. (20) Berland, K. M.; So, P. T. C.; Chen, Y.; Mantulin, W. W.; Gratton, E. Biophys. J. 1996, 71, 410-420.
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These techniques require that both the probe and the target molecules be fluorescently labeled or that a binding assay be performed in which two or more fluorescent probes attach themselves to the target. In some cases, however, it may be undesirable or impossible to attach a label to the target species or to bind two probes to a single target. In this paper, we describe a new technique for performing rapid, multicomponent analyses in a CE system that does not require separation of the analytes. This technique, which we refer to as CE/FCS, combines the selectivity of CE with the sensitivity and rapid analysis times of FCS. A single-molecule confocal fluorescence microscope was used to sequentially detect single Rhodamine 6G (R6G) and R6G-labeled deoxycytosine triphosphate (R6G-dCTP) molecules continuously flowing through a 40-µmi.d. capillary. The average transit times of single molecules through the detection region were measured using autocorrelation analysis. By applying an electric field between the inlet and outlet of the capillary, we were able to increase or decrease the transit times, depending on the magnitude and polarity of the applied field and the electrophoretic mobilities of the analytes. R6G and R6G-dCTP exist in charge states of +1 and -2, respectively, resulting in different electrophoretic mobilities for the two analytes. Therefore, large differences in the transit times were observed for a given applied field. We exploited these differences to measure the relative concentrations of various R6G and R6G-dCTP mixtures with uncertainties of ∼10% using CE/FCS. For analyte concentrations as low as a few tens of picomolar, it was possible to obtain sufficient FCS data to perform the analysis in less than 10 s. Because R6G and R6G-dCTP are comparable in size, analysis of these solutions by diffusional FCS is difficult to perform. However, CE/FCS requires only that the analytes possess different electrophoretic mobilities and thus provides a means to perform multicomponent analyses that would be difficult or impossible using techniques that are based on diffusional FCS. Although other groups have reported on the use of single-molecule microscopy and spectroscopy techniques in combination with CE,5,21-23 this is the first demonstration of FCS as a detection method for multicomponent analysis in a CE system and the first report in which the measurement being made is the transit time of the analyte molecules through a single femtoliter detection volume. EXPERIMENTAL SECTION A schematic of the CE/FCS experimental apparatus is displayed in Figure 1. The analyte solution typically consisted of ∼10-10 M R6G and/or R6G-dCTP dissolved in an aqueous buffer solution. Solutions of dCTP nucleotides covalently bound to R6G via a six-carbon linker were prepared from a 10-4 M stock solution purchased from NEN Life Science Products (Boston, MA). Two different buffer solutions were used to investigate the effects of solvent pH on the analysis: a 1×TE solution (10 mM Tris-HCl, 0.5 mM EDTA, pH 8.0) and a 10 mM Tris-HCl, 2 mM NaCl, 1 mM EDTA solution adjusted to pH 5.5 with dropwise addition of HCl. Laminar flow of the analyte solution through a 32-cm-long, 40-µm-i.d, 105-µm-o.d. fused-silica capillary (Polymicro Technologies, Phoenix, AZ) was established by immersing the inlet of the (21) Chen, D.; Dovichi, N. J. Anal. Chem. 1996, 68, 690-696. (22) Haab, B. B.; Mathies, R. A. Appl. Spectrosc. 1997, 51, 1579-1584. (23) Fister, J. C.; Jacobson, S. C.; Davis, L. M.; Ramsey, J. M. Anal. Chem. 1998, 70, 431-437.
Figure 1. Schematic diagram of the CE/FCS experimental apparatus.
capillary in the analyte solution and pressurizing with N2. The laminar flow rate was precisely controlled by regulating the pressure to between 0 and 10 psig using a pneumatic pressure regulator (Fairchild, Winston-Salem, NC). Electric fields of (150-(625 V/cm were applied between the inlet and outlet of the capillary using a high-voltage power supply (Spellman, Model CZE1000R, Plainview, NY) capable of supplying 0-30 kV with positive or negative polarity. A platinum wire was connected to the high-voltage output of the power supply and immersed in the analyte solution, and a second platinum wire was immersed in the solvent reservoir and connected to the power supply ground through a 774-kΩ resistor. The electrical current through the capillary was monitored by measuring the voltage across this resistor. Typical currents were between 3 µA for an electric field of 150 V/cm and 13 µA for a 625 V/cm electric field. The electrophoresis capillary and the confocal microscope were enclosed inside a Plexiglas box equipped with a safety interlock to the high-voltage power supply. FCS measurements were performed using a home-built singlemolecule confocal fluorescence microscope. An observation window was created in the capillary by burning away a ∼5-mm section of the polyimide coating to expose the fused-silica surface. This section of the capillary was then mounted on a microscope slide and placed beneath a cover slip. A layer of immersion oil was placed between the observation window and the cover slip. Single-molecule fluorescence was induced by focusing the output of a small-frame, cw Ar ion laser (American Laser, model LS1000, Salt Lake City, UT) operating at 514.5 nm into the capillary through the observation window using an oil immersion 120×, 1.3 NA microscope objective to form a detection region defined by the focal volume of the laser beam. The laser power at the sample was typically 0.8 mW. The curvature of the capillary walls introduced distortions to the shape of the detection region from an ideal Gaussian profile due to spherical aberrations and beam astigmatism. These distortions increased as the distance of the detection region from the inner capillary wall increased, so that
positioning the detection region near the center of the capillary resulted in reduced single-molecule detection (SMD) sensitivity. However, positioning the detection region too close to the inner surface of the capillary caused such undesirable effects as interactions between the analyte molecules and the glass surface, as well as greatly reduced flow velocities. We found that by positioning the detection region ∼8 µm from the inner surface of the capillary, we could achieve the best compromise between SMD sensitivity and good flow conditions. Before passing through the microscope objective, the laser beam was collimated and expanded to a diameter of ∼10 mm using a 10× telescope and focused to a small spot 150 mm behind the rear aperture of the objective with a 175-mm focal length lens. The laser beam diameter at the rear of the objective was just large enough to fill the rear aperture. Fluorescence bursts from single molecules flowing through the detection region were collected with the same microscope objective used to focus the excitation laser beam into the capillary. A dichroic beam splitter (CVI Laser, Albuquerque, NM) transmitted the laser beam into the objective and reflected the fluorescence signal to a 200-µm-diameter pinhole placed 150 mm from the rear aperture of the objective. Light passing through the pinhole passed through a 550 ( 15 nm spectral band-pass filter (Omega Optical, Battleboro, VT) and was focused onto a passively quenched silicon avalanche photodiode (APD) single-photon counting detector (EG&G Canada, model SPCM-200-PQ, Vaudreuil, Quebec) using an 11-mm focal length aspheric lens (Thorlabs, Newton, NJ). Autocorrelation analysis of the time-resolved fluorescence signal was performed in real-time by feeding the output of the APD detector into a digital correlator card (ALV Multiple Tau, model ALV5000/E, Langen, Germany) mounted in a Pentium computer. A multichannel scaler (MCS) card (Oxford Instruments, model MCS-II, Oak Ridge, TN), mounted in the same computer, was used to record real-time fluorescence burst data. RESULTS AND DISCUSSION FCS Measurements. The digital correlator accumulates photoelectron pulses from the detector into 288 time bins, with sampling times per bin ranging from 200 ns to several hours. In our case, only time bins below a few tens of seconds were utilized. An autocorrelation function was calculated in real-time for lagtime τ, using symmetric normalization, as follows:
N G(τ) )
N
N
N
t)1
t)1
t)1
∑n(t)n(t + τ) - ∑n(t)∑n(t + τ) N
N
t)1
t)1
(1)
∑n(t)∑n(t + τ) where N is the total number of time bins and n(t) is the number of counts in bin t. This calculation is performed for lag times ranging from 200 ns to a few tens of seconds to generate an autocorrelation curve, which is plotted as a function of τ. The shape of the autocorrelation curve depends on the dimensions of the probe region and the transit times of the analyte molecules through the probe region. For the case of diffusion of the analyte molecules in a single-component solution through a Gaussianshaped detection volume, the experimental autocorrelation curve Analytical Chemistry, Vol. 70, No. 21, November 1, 1998
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Figure 3. Normalized autocorrelation functions from a 10-10 M solution of R6G (b) and a 10-10 M solution of R6G-dCTP (0)with the pressure-driven flow turned off, compared with normalized autocorrelation functions from 10-10 M R6G under conditions of uniform flow. Different flow velocities were obtained by applying 2.5 (O), 5.0 (+), and 10 (]) psig N2 to the inlet of the capillary. The solid curves are from fits to eqs 3 and 4 for the autocorrelation functions obtained with the pressure-driven flow off and on, respectively. The measurement time for each curve was 30 s.
Figure 2. Time-resolved fluorescence signal from a 10-10 M solution of R6G in 1×TE buffer displaying fluorescence bursts from single R6G molecules. The data were collected using an MCS bin width of 50 µs and smoothed using a one-point binomial filtering algorithm. (a) Pressure-driven flow off. (b) Pressure-driven flow initiated by applying 5.0 psig N2 to the inlet of the capillary, resulting in a flow velocity of ∼5.6 mm/s.
is modeled by fitting to the following analytical expression:8
G(τ) ) 1 + A
(
)[
]
1 1 1 + τ/τD 1 + (ω /z )2(τ/τ ) 0 0 D
1/2
(2)
where A is the amplitude, ω0 and z0 are the e-2 radial and axial dimensions of the detection volume, respectively, τD is the transit time of the analyte molecules due to diffusion through the radial dimension, and (ω0/z0)-2τD is the transit time through the axial dimension. Using our single-molecule confocal microscope, we measured the autocorrelation function for a 10-10 M static solution of R6G in water in a slide and cover slip arrangement and obtained an excellent fit of the data to eq 2. The parameters from the fit were τD ) 48 ( 6 µs and (ω0/z0) ) 0.08 ( 0.02. From the relationship τD ) ω02/4D, where D is the diffusion constant of R6G in water (3 × 10-6 cm2/s 24), we obtained ω0 ) 0.24 ( 0.03 µm and z0 ) 3.1 ( 0.2 µm, which corresponds to a detection volume of ∼1.1 fL. Figure 2 displays 80 ms of time-resolved fluorescence counts, binned into 50-µs intervals using the MCS, from a 10-10 M solution of R6G placed inside the capillary. A 1-point binomial filtering algorithm was used to smooth the raw MCS data using Igor Pro data analysis software (Wavemetrics, Lake Oswego, OR). Bursts (24) Hansen, R. L.; Zhu, X. R.; Harris, J. M. Anal. Chem. 1998, 70, 1281-1287.
4466 Analytical Chemistry, Vol. 70, No. 21, November 1, 1998
of photons from single R6G molecules are observed as sharp peaks rising above the background. For the data presented in Figure 2a, the capillary inlet was at atmospheric pressure, so the photon bursts are due to single molecules diffusing in and out of the detection volume. For Figure 2b, the capillary inlet was pressurized to 5.0 psig. Photon bursts, in this case, are due both to single-molecule diffusion and uniform flow of single molecules across the detection volume. It is clear from Figure 2 that pressure-induced flow increases the burst frequency and significantly reduces the transit times of single molecules through the detection volume, as seen from the much narrower burst widths. Below, we describe the FCS technique used to measure the average single-molecule transit times under flow and diffusion conditions. Autocorrelation curves obtained from 10-10 M solutions of R6G and R6G-dCTP placed inside the capillary are displayed in Figure 3. The amplitude of each curve is normalized to 1. The curves denoted by filled circles and open squares were obtained for the R6G and R6G-dCTP solutions, respectively, under diffusion-only conditions. The other curves are due to diffusion and pressuredriven flow of the R6G solution and were obtained by pressurizing the inlet of the capillary to 2.5, 5.0, and 10 psig. The diffusiononly autocorrelation curve for the R6G solution due to excitation through the capillary differed from that obtained due to excitation through the cover slip in two respects. First, the width of the autocorrelation curve was significantly broadened due to excitation through the capillary, indicating a larger detection volume compared to that obtained through the cover slip. Second, the autocorrelation curve fit poorly to the analytical expression for diffusion through a Gaussian-shaped detection volume (eq 2). We attribute these observations to spherical aberration and beam astigmatism, incurred by focusing the laser beam through the curved surface of the capillary, that enlarge the detection volume and distort its shape from an ideal Gaussian profile. Unfortunately, an analytical expression that accounts for these effects is not
straightforward to derive. Rigler and co-workers observed similar effects in their diffusional FCS studies that were caused by increasing the intensity of the excitation laser, which they attributed to distortions in the effective excitation profile introduced by the increased laser power.12 To account for these effects, they used a semiempirical expression to fit the diffusion region of their autocorrelation curves, in which the detection volume was described by a linear combination of two Gaussian distributions. We achieved excellent fits to our diffusion-only autocorrelation curves by using a similar expression (eq 3). In this equation, A
G(τ) ) 1 + A
(
)
1-R R + 1 + τ/τd1 1 + τ/τd2
(3)
is the amplitude of the autocorrelation function (normalized to 1) and R and (1 - R) are the relative fractions of the two diffusion times, τd1 and τd2, respectively. The diffusion times through the axial dimensions could not be determined from our data, so a two-dimensional model was assumed for the Gaussian distributions. The solid curve drawn through the filled circles in Figure 3 is from a least-squares fit of the diffusion-only R6G data to eq 3. In this case, we found R ) 0.72 ( 0.02, τd1 ) 286 ( 25 µs, and τd2 ) 10.8 ( 2.4 µs. In the limiting case where R ) 1, eq 3 reduces to the two-dimensional Gaussian model, with τd1 ) τD. Since the largest contribution to the observed diffusion-only autocorrelation function comes from τd1, we assume that τd1 ≈ τD, which yields an effective value for ω0 of 0.6 µm. A fit of the diffusion-only autocorrelation curve obtained from the R6G-dCTP data to eq 3, displayed as a solid line through the open squares in Figure 3, yielded R ) 0.73 ( 0.02, τd1 ) 383 ( 35 µs, and τd2 ) 10.6 ( 2.4 µs. The larger value of τd1 for R6G-dCTP, compared to τd1 of R6G, is consistent with a longer diffusion time for this analyte. However, the difference in the diffusion times is not sufficient to effectively discriminate between the two analytes by diffusional FCS alone. The autocorrelation curves displayed in Figure 3, taken under conditions of diffusion and pressure driven flow, were obtained for the R6G solution by pressurizing the capillary inlet to 2.5 (open circles), 5.0 (plus signs), and 10 psig (diamonds). Magde, Webb, and Elson derived an analytical expression that models the autocorrelation function for diffusion and uniform flow through a Gaussian-shaped detection volume.10 The solid curves through the experimental data points in Figure 3 are from least-squares fits to a version of this expression that has been modified to account for the nonideal shape of the detection volume (eq 4).
G(τ) ) 1 + A
(
)
R 1-R + × 1 + τ/τd1 1 + τ/τd2
[ ( )(
exp -
τ τF
2
)]
1-R R + 1 + τ/τd1 1 + τ/τd2
(4)
This equation assumes that the dimensions of the detection volume are much smaller than the capillary dimensions so that the flow velocity is uniform across the detection volume. Here, τF is the average transit time for a single molecule due to uniform flow through the detection volume. The fits were performed by fixing R and τd2 to the values obtained from the diffusion-only autocorrelation curves and allowing both τd1 and τF to vary. If
the flow velocity profile was strictly uniform across the detection volume, there would be no coupling between the flow and diffusion terms in eq 4. However, in this case, we find that τd1 does increase and decrease with τF to some extent, indicating some degree of nonuniformity in the flow profile. This may be attributed to enlargement of the axial dimension of the detection volume due to beam aberration. Nevertheless, the coupling between the flow and diffusion terms is small, and we assume that the τF values obtained by fitting to eq 4 represent a close approximation to the uniform flow transit times. The flow velocity of the solution, v, is estimated for each autocorrelation curve using v ) ω0/τF.10 From these analyses, we obtain flow velocities of 2.73, 5.64, and 10.12 mm/s for the 2.5, 5.0, and 10 psig pressure drops, respectively. The relative uncertainties in these measurements is less than ∼5%. To test the validity of the assumptions being made, we calculated the flow velocities for each pressure drop using the expression for laminar flow through a cylindrical capillary (eq 5).25
υ)
∆p 2 (P - F2) 4ηl
(5)
Here, ∆p is the pressure drop across the capillary, η is the viscosity of water at 293 K (0.01 g cm-1 s-1), l is the length of the capillary, Ρ is the capillary radius, and F is the radial distance of the detection region from the central axis of the capillary (typically ∼12 µm). From eq 5, we obtain flow velocities of 3.4, 6.8, and 13.6 mm/s for pressure drops of 2.5, 5.0, and 10 psig, respectively. These flow velocities are only ∼20% larger than those estimated from the autocorrelation analyses, and thus we conclude that the assumption ω0 ≈ 0.6 µm is reasonable to make and that τF from eq 4 is valid. The difficulties described above associated with interpreting the autocorrelation data could be eliminated by performing these measurements in a square-bore capillary or a microfabricated flow channel to reduce the effects of spherical aberration and beam astigmatism. However, the main purpose of this study is to discriminate between two different analytes on the basis of their different autocorrelation functions. As will become apparent, this was accomplished very successfully using the fitting procedures described above. CE/FCS of R6G. When an electric field was applied between the capillary inlet and outlet, the autocorrelation curves from the R6G solutions became narrower or broader, depending on the magnitude and polarity of the applied field, compared to the flowdiffusion autocorrelation curve measured with the field off. This is due to the electroosmotic flow (EOF) rate of the bulk solution and the electrophoretic mobility of the analyte molecules. The EOF flows from the positive to the negative electrode. Therefore, when the electric field polarity is positive, the EOF flows in the same direction as the pressure-induced laminar flow, resulting in a net increase of the flow velocity and a narrower autocorrelation curve. When the polarity is reversed, the EOF flows opposite to the laminar flow, resulting in a reduced flow velocity and a broader autocorrelation curve. Since R6G is a singly charged positive ion, (25) Kachel, V.; Fellner-Feldegg, H.; Menke, E. In Flow Cytometry and Sorting, 2nd ed.; Melamed, M. R., Lindmo, T., Mendelsohn, M. L., Eds.; WileyLiss: New York, 1990; pp 27-44.
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Figure 4. Normalized autocorrelation functions from 5 × 10-10 M solutions of R6G obtained using different applied electric fields across the capillary: (a) solvent pH 8.0; (b) solvent pH 5.5. Flow conditions were achieved by applying 2.5 psig N2 to the inlet of the capillary and applying -625 V/cm (- - - -), -313 (large dashes), 0 (s), +313 V/cm (- ‚ -), and +625 V/cm (small dashes) between the inlet and outlet. The dotted curve was obtained with the pressure-driven flow and the electric field off. The measurement time for each curve was 30 s.
the electrophoretic mobility of the analyte adds another component to the net flow velocity in the same direction as the EOF. Figure 4a displays normalized autocorrelation curves obtained for R6G in the pH 8.0 buffer solution at electric field strengths of +625, +313, 0, -313, and -625 V/cm. These curves were fit to eq 4 to obtain estimated values for τF and v, and the fitted parameters are displayed in Table 1. The quality of the fits was the same as those displayed in Figure 3. For these measurements, the capillary inlet was maintained at a constant pressure of ∼2.5 psig. The dotted curve is the diffusion-only autocorrelation function obtained with the pressure and electric field off and is displayed for comparison. From these measurements, it is apparent that the applied electric fields induced very large changes in the single-molecule transit times. Applying +625 V/cm resulted in a 2.4-fold reduction in τF compared to τF at zero field, from about 202 to 85 µs. This corresponds to an increase in the net flow velocity of 4.05 mm/s, from 2.98 to 7.03 mm/s. A much larger difference in the τF’s was observed by applying -625 V/cm. In this case, τF changed from 202 µs at zero field to ∼1.1 ms, corresponding a 5.6-fold increase. The net flow velocity was reduced by 2.45 mm/s, from 2.98 to 0.53 mm/s. As seen in Figure 4a, the sum of the EOF and the electrophoretic mobility was so large at -625 V/cm that it almost canceled out the pressuredriven flow. 4468 Analytical Chemistry, Vol. 70, No. 21, November 1, 1998
The data in Figure 4b were taken under the same experimental conditions, except that the buffer pH was lowered to 5.5 and the capillary was rinsed with 0.1 M HCl prior to introducing the analyte solution. These data were also analyzed by fitting to eq 4, and the fit parameters are displayed in Table 1. It was shown previously that lowering the pH reduces the EOF.26 This is evident from the much smaller differences between τF at zero field and the τF’s obtained with the field applied, compared to the results at pH 8.0. With the pH at 5.5, τF changed from ∼203 µs at zero field to 125 µs at +625 V/cm and 347 µs at -625 V/cm, corresponding to a ∼1.5-fold difference for both positive and negative polarities. The net flow velocity increased by 1.85 mm/s and decreased by 1.22 mm/s for positive and negative polarities, respectively. Figure 5 summarizes the results obtained for R6G in the pH 8.0 and 5.5 buffers. Here, the net flow velocities and inverse τF’s, estimated from analysis of the autocorrelation curves, are plotted against applied electric field strengths ranging from 156 to 625 V/cm with both positive and negative polarities. It is interesting that, for the same magnitude of the applied electric field, the displacement in the flow velocity from the zero field case is larger for positive than for negative polarity, indicating that the sum of the EOF velocity and the electrophoretic mobility of R6G makes a larger contribution to the net flow velocity when in the same direction as the pressure-driven flow. CE/FCS of R6G-dCTP. The R6G-dCTP complex possesses a net charge of -2, so the direction of the electrophoretic mobility of this analyte is opposite the EOF and is, therefore, antiparallel to the pressure-driven flow when a positive polarity electric field is applied and parallel to the pressure-driven flow when a negative polarity electric field is applied. Figure 6a displays normalized autocorrelation functions obtained from a 10-10 M solution of R6GdCTP in a pH 8.0 buffer. These autocorrelation curves were obtained with the capillary inlet pressurized to ∼2.5 psig and applied electric fields of +625, 0, and -625 V/cm. The diffusiononly autocorrelation function (dotted curve) is also shown for comparison. The parameters from a fit of the autocorrelation curves to eq 4 are presented in Table 2. At pH 8.0, the EOF velocity is larger than the electrophoretic mobility of the analyte. Therefore, the net flow velocity increases with the application of a positive polarity electric field and decreases for a negative polarity field, as was also the case for free R6G. However, the displacements in τF from the zero-field condition are significantly smaller than those observed for R6G at the same pH, since the electrophoretic mobility of R6G-dCTP partly cancels the EOF. In this case, τF changed from ∼207 µs at zero field to 127 µs at +625 V/cm and 315 µs at -625 V/cm. This corresponds to an increase in the net flow velocity of 1.82 mm/s for positive polarity and a decrease of 0.99 mm/s for negative polarity. Here again, the displacement in the net flow velocity is largest with the application of a positive polarity electric field. Figure 6b displays the autocorrelation functions obtained after the capillary is rinsed with 0.1 M HCl and a R6G-dCTP solution dissolved in pH 5.5 buffer is introduced. Under these conditions, the application of a positive polarity electric field of 625 V/cm caused essentially no displacement in the autocorrelation curve from the curve measured at zero field. This is an indication that, (26) Lambert, W. J.; Middleton, D. L. Anal. Chem. 1990, 62, 1585-1587.
Table 1. Least-Squares Fit Parameters for the Autocorrelation Functions of the Pure R6G Solutionsa,b applied electric field, V/cm parameter pH 8.0 τd1 (µs) τF (µs) v (mm/s)c pH 5.5 τd1 (µs) τF (µs) v (mm/s)c
0
-625
-313
+313
+625
226.8 ( 8.1 201.7 ( 5.5 2.98 ( 0.05
263.4 ( 3.4 1133 ( 150 0.529 ( 0.07
282.4 ( 3.4 330.6 ( 18.0 1.81 ( 0.06
195.7 ( 4.3 130.6 ( 2.3 4.59 ( 0.05
138.9 ( 3.0 85.4 ( 1.1 7.03 ( 0.06
315.2 ( 11.7 203.2 ( 4.0 2.95 ( 0.04
286.0 ( 14.1 347.2 ( 8.7 1.73 ( 0.04
296.5 ( 14.6 230.9 ( 7.4 2.60 ( 0.05
309.3 ( 12.6 170.1 ( 3.8 3.53 ( 0.05
203.9 ( 8.8 125.0 ( 2.0 4.80 ( 0.05
a Relative uncertainties are at 95% confidence. b R and τ were fixed to their average values of 0.72 ( 0.01 and 10.8 ( 2.4 µs, respectively. c Flow d2 velocities were estimated by assuming ω0 ) 0.6 µm.
Figure 5. Net flow velocities and inverse transit times, estimated from the autocorrelation analysis, of R6G: pH 8.0 (O) and pH 5.5 (×) vs the applied electric field.
at pH 5.5, the EOF velocity is equal and opposite to the electrophoretic mobility of the analyte, and so there is essentially no change in the net flow velocity with the application of an electric field under these conditions. When the polarity of the electric field was reversed, τF became smaller compared to the zero-field value, indicating a net increase in the flow velocity. For an applied field of -625 V/cm, τF was reduced to 152 µs from the zero-field value of 206 µs, corresponding to a net increase in the flow velocity of 1.04 mm/s. In this case, the electrophoretic mobility of the analyte is directed parallel to the pressure-driven flow and possesses a magnitude that is larger than the EOF flowing antiparallel to the pressure-driven flow. It would appear that lowering the pH from 8.0 to 5.5 reduces the EOF, but probably has very little effect on the electrophoretic mobilities of the analyte molecules. Figure 7 plots the estimated flow velocities and inverse τF’s determined from the autocorrelation analyses obtained for several different electric field strengths to summarize the R6GdCTP results in the pH 8.0 and 5.5 buffers. Two-Component Analysis of R6G/R6G-dCTP Mixtures by CE/FCS. The autocorrelation curve for a pure solution of R6GdCTP with no applied electric field is essentially indistinguishable from that of a pure R6G solution under conditions of pressuredriven flow. However, comparison of Figures 5 and 7 reveals that, in the presence of an electric field, the net flow velocities and the single-molecule transit times depend on the electrophoretic mobilities of the analytes and are significantly different for R6G
Figure 6. Normalized autocorrelation functions from 5 × 10-10 M solutions of R6G-dCTP obtained using different applied electric fields across the capillary: (a) solvent pH 8.0; (b) solvent pH 5.5. Flow conditions were achieved by applying 2.5 psig N2 to the inlet of the capillary and applying -625 (- - - -), 0 (s), and +625 (- - -) V/cm between the inlet and outlet. The dotted curve was obtained with the pressure-driven flow and the electric field off. The measurement time for each curve was 30 s.
and R6G-dCTP. Therefore, it is possible to determine the relative concentrations of a R6G/R6G-dCTP mixture from FCS measurements obtained in the presence of an electric field. The best discrimination between the two analytes is achieved under conditions in which the difference between τF of R6G and τF of R6G-dCTP is maximized. Of all the different sets of conditions investigated in this study (pressure-driven flow velocity, electric field magnitude and polarity, pH, pressure-driven flow on or off), we found the largest difference between the transit times to occur with a pressure-driven flow velocity of ∼2.9 mm/s (capillary inlet pressurized to ∼2.5 psig), an applied electric field of -625 V/cm, Analytical Chemistry, Vol. 70, No. 21, November 1, 1998
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Table 2. Least-Squares Fit Parameters for the Autocorrelation Functions of Pure R6G-dCTP Solutionsa,b applied electric field, V/cm parameter pH 8.0 τd1 (µs) τF (µs) v (mm/s)c pH 5.5 τd1 (µs) τF (µs) v (mm/s)c
0
-625
+625
316.0 ( 12.1 206.6 ( 5.0 2.90 ( 0.05
361.2 ( 8.4 314.5 ( 12.3 1.91 ( 0.06
184.9 ( 4.6 127.0 ( 2.5 4.72 ( 0.06
305.4 ( 9.1 206.3 ( 3.2 2.91 ( 0.03
257.5 ( 11.3 152.0 ( 2.9 3.95 ( 0.05
272.1 ( 16.2 199.0 ( 5.2 3.01 ( 0.05
a Relative uncertainties are at 95% confidence. b R and τ were fixed d2 to their average values of 0.73 ( 0.02 and 10.6 ( 2.4 µs, respectively. c Flow velocities were estimated by assuming ω ) 0.6 µm. 0
Figure 7. Net flow velocities and inverse transit times, estimated from autocorrelation analysis, of R6G-dCTP: pH 8.0 (O) and pH 5.5 (×) vs the applied electric field.
Figure 8. Average transit times due to uniform flow, estimated from autocorrelation analysis, obtained from a pure solution of R6G (O) and a pure solution of R6G-dCTP (×) in pH 8.0 buffer, vs the applied electric field.
and a buffer pH of 8.0. Figure 8 illustrates this by plotting τF of pure R6G and R6G-dCTP in the pH 8.0 buffer as a function of the applied field. With an applied field of -625 V/cm, τF of R6G is ∼1100 µs, compared to 274 µs for R6G-dCTP. By contrast, τF is ∼85 µs for R6G and 127 µs for R6G-dCTP at +625 V/cm. 4470 Analytical Chemistry, Vol. 70, No. 21, November 1, 1998
Figure 9. Normalized autocorrelation functions from solutions containing different relative concentrations of R6G and R6G-dCTP in 1×TE buffer (pH 8.0). Flow conditions were achieved by applying 2.5 psig N2 to the inlet of the capillary. The applied electric field was (a) +625 V/cm and (b) -625 V/cm. The solution concentrations were 5 × 10-10 M R6G-dCTP (• • •), 5 × 10-10 M R6G-dCTP and 1.3 × 10-10 M R6G (small dashes); 10-10 M R6G-dCTP and 10-10 M R6G (- ‚ -), 1.3 × 10-10 M R6G-dCTP and 5 × 10-10 M R6G (- - - -), and 5 × 10-10 M R6G (large dashes). The estimated uncertainty in the concentrations is 5%. The solid curves were obtained from the 5 × 10-10 M R6G solution with the electric field off. The measurement time for each curve was 30 s.
To illustrate the capability of CE/FCS for performing twocomponent analysis, we measured the autocorrelation functions of three different R6G and R6G-dCTP mixtures prepared from the stock solutions. The solution concentrations were 1.3 × 10-10 M R6G and 5 × 10-10 M R6G-dCTP (solution 1), 10-10 M R6G and 10-10 M R6G-dCTP (solution 2), and 5 × 10-10 M R6G and 1.3 × 10-10 M R6G-dCTP (solution 3). Errors in these concentrations are estimated to be ∼5%, due to dilution errors and the uncertainty in the concentration of the stock solutions. The relative R6G concentrations for solutions 1-3 were 0.21 ( 0.02, 0.50 ( 0.05, and 0.79 ( 0.07, respectively. The solvent pH was 8.0 for all solutions. Figure 9 plots the normalized autocorrelation curves obtained from a pure R6G-dCTP solution, solutions 1-3, and a pure R6G solution. The pressure drop across the capillary was ∼2.5 psig, and the applied electric field was +625 V/cm for Figure 9a and -625 V/cm for Figure 9b. The solid curves are from a pure R6G solution obtained with the electric field off and are shown for comparison. A steady progression from longer to shorter transit times can be seen for the positive polarity electric field and from shorter to longer transit times for the negative polarity electric field with increasing relative R6G concentration.
Table 3. CE/FCS Measurements of the Relative R6G Concentrations for Three Solutions of R6G and R6G-dCTPa,b rel R6G concn soln
-625 V/cm
+625 V/cm
CR6Gc
as prepared
1 2 3
0.25 ( 0.05 0.53 ( 0.03 0.73 ( 0.03
0.27 ( 0.03 0.55 ( 0.08 0.83 ( 0.03
0.26 ( 0.03 0.54 ( 0.05 0.79 ( 0.06
0.21 ( 0.02 0.50 ( 0.05 0.79 ( 0.07
a Uncertainties are at 95% confidence. b The solvent was 1×TE buffer (pH 8.0). c Relative R6G concentration obtained by averaging together the negative and positive polarity results.
As expected, the discrimination between the autocorrelation curves for the different solution concentrations was largest with the negative polarity field, but good discrimination was also achieved with positive polarity, despite the much smaller difference in the τF’s between R6G and R6G-dCTP. The autocorrelation functions in Figure 9 were analyzed to obtain the relative concentrations of each solution by fitting to a linear combination of the single-component autocorrelation curves (eq 6).8 Here, CR6G is the relative concentration of R6G, (1 - CR6G)
G(τ) ) 1 + A{CR6G[GR6G(τ) - 1] + (1 - CR6G)[GdCTP(τ) - 1]} (6)
is the relative concentration of R6G-dCTP, and GR6G(τ) and GdCTP(τ) are the single-component autocorrelation functions from eq 4 (amplitudes normalized to 1) for R6G and R6G-dCTP, respectively. For each autocorrelation curve in Figure 9, the parameters of GR6G(τ) and GdCTP(τ) were fixed to the values in Tables 1 and 2 and A and CR6G were varied. The quality of the fits was comparable to those displayed in Figure 3. Table 3 lists the relative R6G concentrations obtained for each solution from the positive polarity and the negative polarity data. The final values of CR6G, obtained by averaging together all the data from the negative and positive polarity measurements, were 0.26 ( 0.03, 0.54 ( 0.05, and 0.79 ( 0.06 for solutions 1-3, respectively. Thus, the CE/FCS measurements reproduced the relative R6G concentration for each solution to within experimental error. An alternative method for analyzing the binary mixture is to fit the autocorrelation functions to linear combinations of the experimental single-component autocorrelation data rather than to the fits to eq 4. We have done this with some of our data and achieved essentially the same results for the relative R6G concentrations and the same level of precision as reported above. This fitting procedure is useful for complex situations in which the autocorrelation functions are more difficult to model, but it provides no physical insight regarding transit times, flow rates, etc. The very large difference in the transit times observed for R6G and R6G-dCTP suggests that CE/FCS will be applicable to a variety of systems for which the electrophoretic mobilities of the analytes do not differ to such a large extent. For example, R6G and Rhodamine B (Rh-B) are both fluorescent rhodamine derivatives with nearly equal molecular weights. At pH 8.0 Rh-B is predominantly zwitterionic with a net charge of zero and thus
can be separated from R6G by CE at this pH. Using CE/FCS, we were able to observe measurable differences in the transit times from pure solutions of R6G and Rh-B in the pH 8.0 buffer under experimental conditions similar to those described above. With a pressure-driven flow velocity of 3.02 ( 0.05 mm/s at zero field, we found that the net flow velocities reduced to 0.60 ( 0.04 and 0.32 ( 0.02 mm/s for the R6G and Rh-B solutions, respectively, due to the application of a -625 V/cm electric field. The values of τF were 1.00 ( 0.07 ms for R6G and 1.88 ( 0.12 ms for Rh-B, compared to 198.7 ( 3.3 µs for both analytes at zero field. This is a large enough difference in the transit times to analyze a binary mixture of R6G and Rh-B by CE/FCS. A smaller, but still measurable, difference in the transit times was observed using a +625 V/cm electric field. Under these conditions, the net flow velocities of the R6G and Rh-B solutions increased to 6.89 ( 0.10 and 6.47 ( 0.08 mm/s, respectively, corresponding to τF’s of 87.1 ( 1.3 µs for R6G and 92.7 ( 1.1 µs for Rh-B. CONCLUSIONS We have combined CE with FCS to perform rapid multicomponent analysis in a CE system without separating the analytes. Under the conditions described in this paper, analysis times as low as 10 s were achieved, compared to minutes or tens of minutes that would be required to perform a CE separation. FCS is most sensitive when applied to single-molecule microscopy experiments, in which the number of molecules present in the detection volume fluctuates between zero and one, and fluorescence bursts from single molecules are detected above background. These were the conditions used for the experiments reported here. However, FCS can also be applied to solution concentrations as high as the micromolar range, in which the detection volume is occupied by several hundred molecules. For higher analyte concentrations, the analysis times could be even further reduced to less than 1 s. Furthermore, analyte molecules that do not fluoresce strongly enough to be detected at the single-molecule level can still be studied by FCS, so long as the population fluctuations are detectable above the average fluorescence signal.27 Therefore, the CE/FCS technique is potentially applicable to a much broader range of experimental conditions than those described here. We anticipate that this technique will be especially useful for performing probe-target binding assays under conditions in which the diffusion rates of the bound and unbound probe molecules are not significantly different. ACKNOWLEDGMENT This research was supported by the Los Alamos Center for Human Genome Studies under United States Department of Energy Contract W-7405-ENG-36. We thank W. Patrick Ambrose, Peter M. Goodwin, and Yongseong Kim for helpful suggestions and discussion and Harvey Nutter for his expert technical assistance.
Received for review July 13, 1998. Accepted August 20, 1998. AC980768Q (27) La Clair, J. J. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 1623-1628.
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