Anal. Chem. 1997, 69, 2426-2433
Two-Channel Sequential Single-Molecule Measurement Robert D. Guenard,† Leslie A. King, Benjamin W. Smith, and James D. Winefordner*
Department of Chemistry, University of Florida, Gainesville, Florida 32611-7200
Experimental results are given which demonstrate the sequential detection of single molecules with a measurement efficiency of near unity. IR140 dye molecules are detected in sequential probe volumes within a flowing stream through a 9 µm i.d. capillary. The measurement of single molecules was confirmed by means of autocorrelation, photobleaching, visual observation, and crosscorrelation analysis. The number of single molecules photobleached prior to being measured in the second probe region was in excellent agreement with the bulk studies described by a photodestruction curve. A crosscorrelation peak with a temporal delay corresponding to the interprobe volume transit time and a width in agreement with parabolic flow give a clear indication of sequential detection. The near unity measurement efficiencies for both channels indicates the great potential for rapid quantitative analysis of dilute solutions. Since the first direct observation of a photon burst from a single fluorophore in solution in 1990,1 there have been many researchers who have achieved single-molecule sensitivity through laserinduced fluorescence. Several instrumental approaches have been used to accomplish single-molecule detection (SMD) including the following: a levitated microdroplet technique,2-4 pulsed laser, time-gated detection,5-8 confocal microscopy,9-11 two-photonexcited fluorescence,12 and near-infrared fluorescence.13-15 Information gained from the analysis depends upon the approach taken
to detect individual molecules. For example, the microscopy techniques generally have higher signal-to-noise ratios (SNR) compared to methods in which the molecule is detected in a flowing stream. Microscopy methods typically use high numerical aperture microscope objectives (NA > 1) to focus the excitation light and to collect the fluorescence, yielding probe volumes of 1 fL or less. Because the SNR of a SMD technique relates inversely with the probe volume, microscopy techniques will inherently have higher SNRs. In fact, using confocal microscopy, Nie and coworkers were able to observe individual molecules in the probe region in real time with light and dark gaps in the fluorescence signal corresponding to diffusion of the molecule and intersystem crossing to a dark triplet state.16 However, the high SNRs gained with such small probe volumes are done at the expense of sample throughput. With molecular transit times through the laser beam on the order of a few milliseconds, flowing techniques have the capability to sample at very high rates (up to a few thousand molecules per second) with continuous sampling.17 As pointed out by Chen and Dovichi, to obtain a low relative precision in quantitative ultrasensitive analysis, which is by nature shot noise limited, many molecules must be counted.18 Therefore, in terms of quantitative analysis, flowing stream techniques have a significant advantage over solvent static methods in which the sample is a droplet and observation of the molecule is dictated by its random walk through the solution. Rigler and co-workers have addressed this sampling problem by placing a droplet sample in a multipolar electrical trap so that charged particles can be translated across the probe region under the influence of an electric field.9,19 Despite this ability to control the motion of the molecule through the probe volume, the rate of analysis is limited due to the time required to change the small sample droplet. Winefordner and Stevenson have developed general theoretical framework to describe the overall efficiency of the detection of a single molecule in a flowing stream.20-22 In that work, they defined a measurement efficiency (m) which accounted for transporting the analyte to the probe region, the efficiency of interrogating the sample with a laser beam, and detecting it while
† Current address: Dow Chemical, Analytical and Engineering Services, 2301 N. Brazosport Blvd., B-1463, Freeport, TX 77541-3257. (1) Shera, E. B.; Seitzinger, N. K.; Davis, L. M.; Keller, R. A.; Soper, S. A. Chem. Phys. Lett. 1990, 174, 553-557. (2) Whitten, W. B.; Ramsey, J. M.; Arnold, S.; Bronk, B. V. Anal. Chem. 1991, 63, 1027-1031. (3) Ng, K. C.; Whitten, W. B.; Arnold, S.; Ramsey, J. M. Anal. Chem. 1992, 64, 2914-2919. (4) Barnes, M. D.; Ng, K. C.; Whitten, W. B.; Ramsey, J. M. Anal. Chem. 1993, 65, 2360-2365. (5) Soper, S. A.; Davis, L. M.; Shera, E. B. J. Opt. Soc. Am. B. 1992, 9, 17611769. (6) Wilkerson, C. W.; Goodwin, P. M.; Ambrose, W. P.; Martin, J. C.; Keller, R. A. Appl. Phys. Lett. 1993, 62, 2030-2032. (7) Li, L. Q.; Davis, L. M. Rev. Sci. Instrumen. 1993, 64, 1524-1529. (8) Affleck, R. L.; Ambrose, W. P.; Demas, J. N.; Goodwin, P. M.; Schecker, J. A.; Wu, M.; Keller, R. A. Anal. Chem. 1996, 68, 2270-2276. (9) Eigen, M.; Rigler, R. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 5740-5747. (10) Nie, S.; Chiu, D. T.; Zare, R. N. Science, 1994, 266, 1018-1021. (11) Schmidt, T. H.; Schultz, G. J.; Baumgartner, W.; Gruber, H. J.; Schindler, H. Proc. Natl. Acad. Sci. U.S.A., 1996, 93, 2626-2629. (12) Mertz, J.; Xu, C.; Webb, W. W. Opt. Lett. 1995, 24, 2532-2534. (13) Soper, S. A.; Mattingly, Q. L.; Vegnuta, P. Anal. Chem. 1993, 65, 740-747. (14) Lee, Y. H.; Maus, R. G.; Smith, B. W.; Winefordner, J. D. Anal. Chem. 1994, 66, 4142-4149. (15) Soper, S. A.; Lengendre, B. L., Jr.; Huang, J. Chem. Phys. Lett. 1995, 237, 339-345.
(16) Nie, S.; Chiu, D. T.; Zare, R. N. Anal. Chem. 1995, 67, 2849-2857. (17) Ambrose, W. P.; Goodwin, P. M.; Jett, J. H.; Johnson, M. E.; Martin, J. C.; Marrone, B. L.; Schecker, J. A.; Wilkerson, C. W.; Keller, R. A.; Haces, A.; Shih, P. J.; Hardings, J. D. Ber. Bunsenges. Phys. Chem. 1993, 97, 15351542. (18) Chen, D. Y.; Dovichi, N. J. Anal. Chem. 1996, 68, 690-696. (19) Rigler, R. J. Biotechnol. 1995, 41, 177-186. (20) Stevenson, C. L.; Winefordner, J. D. Appl. Spectrosc. 1991, 45, 1217-1224. (21) Stevenson, C. L.; Winefordner, J. D. Appl. Spectrosc. 1992, 46, 407-419. (22) Stevenson, C. L.; Winefordner, J. D. Appl. Spectrosc. 1992, 46, 715-724.
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© 1997 American Chemical Society
in the laser volume. The measurement efficiency is given by
m ) T pd
(1)
where T is the transport efficiency of the sample from the point of introduction to the probe region, p is the laser probing efficiency, which combines the temporal (t) and the spatial (s) probing efficiencies, and d is the detection efficiency. The spatial probing efficiency accounts for the loss of molecules not passing through the probe volume. Temporal probing efficiency accounts for the loss of signal due to the duty cycle of the laser; a continuous-wave laser or one with a repetition rate such that the molecule would interact with the laser at least once during its transit time would have a temporal probing efficiency of unity. In their model, the detection efficiency is defined as the probability of observing a signal from a molecule above the background as it passes through the probe volume. As can be seen from the model, the detection efficiency differs dramatically from the measurement efficiency. This concept is important in terms of analyzing samples by SMD in which molecules in the sample must be accurately counted. Single-molecule detection in a flowing stream has been performed in a sheath flow cuvette7,8,18,23,24 and in capillaries.1,5,13-15,25 Interesting SMD studies in flowing streams have included measurements of the fluorescence lifetime of single molecules,6,26 sizing of DNA fragments,17,23,27 determination of thermodynamic and photophysical properties,15 and molecular identification based on their emission spectra5 and characteristic electrophoretic velocity.27,28 One of the main drawbacks of these flowing techniques is that the optically defined probe volume is smaller than the flow cell itself, so that many of the molecules in the sample are not probed by the laser; i.e., the probing efficiency is less than 1. This is done in order to minimize scattering from refractive index gradients which occurs at air/cell and solvent/ cell interfaces. Thus, the overall measurement efficiency of the sample is less than 1 even if the detection efficiency is unity. In the broad scope of high-speed quantitative analysis, this means that, at a given flow rate, a higher volume of solution must be sampled to obtain the desired precision. Furthermore, without 100% efficient laser interrogation of the flow cell, accurate molecule counting for such applications as DNA sequencing and molecular sorting are precluded. Li and Davis have addressed this problem by decreasing the size of the hydrodynamically focused stream to below that of the laser spot size.29 The improvements made increased the overall measurement efficiency to 80%, limited only by the photobleaching of the molecule and not diffusional losses out of the probe region. Lee and co-workers in our laboratory were able to achieve a near-unity measurement efficiency by the on-column detection of the near-infrared dye IR 140 with submillisecond transit times.14 The probe volume (1 pL) was defined by the inner diameter of a microcapillary (11 µm i.d.) and the waist of the laser beam of the same size. In this manner, they (23) Castro, A.; Fairfield, F. R.; Shera, E. B. Anal. Chem. 1993, 65, 849-852. (24) Petty, J. T.; Johnson, M. E.; Goodwin, P. M.; Martin, J. C.; Jett, J. H.; Keller, R. A. Anal. Chem. 1995, 67, 1755-1761. (25) Haab, B. B.; Mathies, R. A. Anal. Chem. 1995, 67, 3253-3260. (26) Tellinghuisen, J.; Goodwin, P. M.; Ambrose, W. P.; Martin, J. C.; Keller, R. A. Anal. Chem. 1994, 66, 64-72. (27) Castro, A.; Shera, E. B. Appl. Opt. 1995, 34, 3218-3222. (28) Castro, A.; Shera, E. B. Anal. Chem. 1995, 67, 3181-3186. (29) Li, L. Q.; Davis, L. M. Appl. Opt. 1995, 34, 3208-3217
Figure 1. Experimental apparatus for two-channel sequential singlemolecule measurement.
were able to fill the flow cell with laser light and achieve 100% probing efficiency of the flowing stream. Specular scatter from the capillary under these conditions was very significant, and conventional methods of scatter rejection were not sufficient to enable the detection of fluorescence from single molecules. Through the use of a novel atomic-based spectral filter placed between the capillary and the detector, the laser scatter was attenuated over 8 orders of magnitude, allowing the detection of single IR 140 molecules. A tunable, continuous-wave, narrow-band Ti-sapphire laser was tuned to an absorption line of a saturated vapor of rubidium metal contained within a quartz cell. The method is based on the premise that the laser line is narrower than the absorption profile of the metal so that laser scatter is attenuated to a large extent. Detailed theoretical and experimental characterization studies were performed in order to maximize the performance of the metal vapor filter.30 Furthermore, this technique relied on the advantages gained in the reduction of background Raman scatter and fluorescence when working in the near-IR.13 Despite all of its analytical advantages, obtaining nearunity measurement efficiency has come at the expense of a lower SNR compared with other SMD techniques. However, the SNR was high enough so that a very high detection efficiency was maintained (97%). We report here the sequential detection of individual molecules as they flow through two probe regions based on the technique developed by Lee and co-workers. IR 140 dye molecules were detected in sequential probe volumes while flowing in laminar fashion through a 9 µm i.d. capillary. Preliminary studies on flow, characterization of the sensitivity of each channel, and detection of sequential single molecules will be presented. Sequential detection confirmation was accomplished with visual matching, calculated interprobe volume transit time, and cross-correlation analysis. Because of the high measurement efficiency obtained in these studies (>95%), molecule observations will be referred to as single-molecule measurement (SMM), i.e., an m of near unity. EXPERIMENTAL SECTION Instrumentation. Sequential on-column single-molecule measurement (SMM) was accomplished using the apparatus shown in Figure 1. The all-lines output of an argon ion laser (Model (30) Guenard, R. D.; Lee, Y. H.; Bolshov, M.; Hueber, D.; Smith, B. W.; Winefordner, J. D. Appl. Spectrosc. 1996, 50, 188-198
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Figure 2. Closeup view of capillary holder and optical configuration.
2060, Spectra-Physics, Mountainview, CA) was used to pump a single-mode, tunable, continuous-wave Ti-sapphire laser (Schwartz Electro-Optics, Inc., Orlando, FL). Operating in the ring configuration, the Ti-sapphire laser had a spectral line width of less than 40 MHz31 (0.081 pm fwhm at 780.1 nm). To attenuate broadband Ti-sapphire luminescence occurring within the divergence of the beam, a narrow-bandpass interference filter (∆λ ) 0.18 nm fwhm at 780.1 nm, Omega Optical, Brattleboro, VT) was used. A 50/50 beam splitter (Melles Griot, Irvine, CA) was used to split the Ti-sapphire beam. The beam was focused onto the capillary (i.d. 9 µm, o.d. 150 µm; Polymicro Technologies, Phoenix, AZ) using singlet lenses (CVI, Orlando, FL) mounted on precision x-y stages (461-XY-M, Newport, Irvine, CA). Solutions were forced through the capillary with a stainless steel pressure bomb using helium. A split-tee configuration with a branching ratio of ∼200 was used to assure laminar flow in the capillary and allow rapid exchange of solutions. An in-house-constructed capillary mount was used to hold the capillary taut and allowed the optics to be maneuvered in the limited space near the capillary (see Figure 2). As can be seen in Figure 2, the fluorescence was collected orthogonally to the laser axis (x) and the capillary axis (z). Light from the capillary was collected with microscope objectives (0.65 NA 40×, Melles Griot, Irvine, CA) which were mounted on precision X-Y and ∆z positioners (Newport). Collimated light from MO1 was passed through a rubidium metal vapor filter (Rb-MVF) to selectively attenuate the significant scattered laser resonant radiation from the capillary. Details of the operation and characteristics of the MVF are published elsewhere.30 The MVF cell (Opthos, Rockville, MD) was heated to ∼150 °C in order to achieve a significant number density of rubidium atoms. The Ti-sapphire laser was tuned to the 52P3/2 (780.023 nm) ground-state transition of the rubidium in the MVF using the intracavity birefringent filter and Fabry-Perot etalon within the Ti-sapphire laser. A nitrogen fill gas (500 Torr) within the MVF cell broadens the rubidium absorption line (calculated Voigt fwhm, 2.19 pm) and quenches fluorescence. Using the Tisapphire/Rb-MVF combination, scattered specular and Rayleigh radiation was attenuated by over 8 orders of magnitude. Radiation not blocked by the MVF, such as background fluorescence and capillary and solvent Raman, was filtered using an interference filter centered at 830 nm (10 nm fwhm (Melles Griot). The light was then refocused onto a fiber-optic pigtail (100 µm core diameter, Canstar, ON, Canada) using a second 40× microscope (31) Schwartz Electro-Optics, Inc., Orlando, FL, measured over a 1 s interval.
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objective (0.65 NA; Melles Griot). Fiber optic cables were coupled to the single-photon avalanche photodiode detectors (SPCM-200PQ, EG&G Optoelectronic, Vaudreuil, Canada) with prealigned FC-type connectors. Dark counts of 25-80 counts/s and photon efficiencies of 25% at 830 nm were observed with the single-photon avalanche photodiodes (SPAPD) used in this work. Digital TTL pulses from the SPAPDs were counted using an on-board counter/ timer board (CTM-05, Keithley Metrabyte, Taunton, MA) and processed with an in-house written program. Autocorrelation and cross-correlation calculations were performed using DaDisp 4.0 SE software running on a pentium-PC. Reagents and Chemicals. The fluorophore used in this research was the dye IR 140 [chemical name, 5,5′-dichloro-11(diphenylamino)-3-3′-10,12-ethylenethiatricarbocyanine perchlorate, fw ) 779; Exciton Chemical Co., Dayton, OH) in a methanol solution (Optima grade, Fisher Scientific, Orlando, FL). Serial dilutions of a 10 µM solution were made daily to minimize photobleaching of the molecules prior to analysis. By manipulating the optics mounted on precision stages, the optical alignment was optimized by maximizing the fluorescence signal of a 1 nM IR 140 solution. Between dye and blank runs, the capillary was rinsed with a methanolic (75%) 1 M NaOH solution. To prevent capillary blockage, all solutions were filtered through a 0.2 µm nylon filter.
RESULTS AND DISCUSSION Flow Studies. In previous work with our apparatus, solutions were pumped through the capillary using a high-precision syringe pump.14 Due to the long flow stabilization times (>30 min) and small reservoir volumes (100 µL), the pump was changed to a pressure bomb-type pump. Rapid flow stabilization, easy sample exchange, large sample volumes (>4 mL), and mechanically noiseless flow were obtained using the pressure pump. To obtain accurate average linear flow velocities at various pressures, the pressure bomb was calibrated. The flow rate was calculated using the Hagen-Poiseuille equation;32 however, to assure a precise calibration, linear velocities were also determined experimentally. A typical way to experimentally determine the flow rate for this experimental configuration would be to perform a flow injection experiment. This would entail installing an injector valve, injecting a sample plug onto the column, and then timing the zone over the distance traveled. To maintain the simplicity of the apparatus, a method was desired that did not require any additional plumbing to the current apparatus. A unique method was devised to measure average linear flow velocities utilizing the two-channel configuration. With a dilute dye solution (1.0 nM) flowing through the capillary at a given pressure, the fluorescence signal in both channels was monitored. The signal obtained in the second channel was lower under equivalent channel conditions due to the occurrence of photobleaching of the dye as it passed through the first probe region. This phenomenon was used to calibrate the flow in the capillary as a function of pressure drop. By rapidly blocking the first laser beam, the signal rise in detector two (see Figure 3) can give information as to the average linear flow velocity. This method is similar to injections performed by optical gating in high-speed (32) Giddings, J. C. Unified Separation Science; John Wiley and Sons: New York, 1991; p 60.
Figure 3. Two-channel fluorescence data used in flow studies. Laser beam 1 blocked at ∼750 ms. Note rise in signal 2 and the delay time resulting before rise occurs.
capillary electrophoresis33,34 and liquid chromatography.35 The time delay (dt) and extent of the rise in the signal (dS) on channel 2 reflected the velocity of the solution passing through the capillary. With increased pressure on the pressure bomb, the time delay will decrease due to increased solution velocity. Under the experimental conditions, the solutions flow through the capillary in laminar fashion with a parabolic profile. Therefore, the frontal chromatogram of nonphotobleached molecules reaching the second probe region first are at the center of the flow profile within the capillary and are flowing at the maximum velocity (vmax). The maximum velocity is obtained by taking the interprobe volume distance (∆z) and dividing it by the delay time (dt) taken from the two-channel fluorescence data. The ∆z value was obtained by translating the channel 1 microscope objective to the channel 2 probe volume while the fluorescence signal was monitored. Once the signal was maximized at the channel 2 probe region, the interprobe volume distance (2.784 mm) was read off the vernier on the translation stage to a precision of (0.001 mm. The average linear velocity (〈v〉) was related to the maximum velocity by
〈v〉 ) vmax/2
(2)
The calibration plot obtained in this manner correlated well with one calculated using the Hagen-Poiseuille model. The fluorescence signal change (dS) in channel 2 decreased with increasing flow rate. This was due to the shorter residence time of the dye in the probe which decreased the percentage of molecules undergoing photobleaching. A photodestruction curve, which relates the amount of photobleaching to linear velocity, was constructed for IR 140 using an approach devised by Stryer et al.36,37 and Larson et al.38 (see Figure 4). The theoretical curve (33) Monnig, C. A.; Jorgenson, J. W. Anal. Chem. 1991, 63, 802-807 (34) Moore, A. W.; Jorgenson, J. W. Anal. Chem. 1993, 65, 3550-3560 (35) Monnig, C. A.; Dohmeier, D. M.; Jorgenson, J. W. Anal. Chem. 1991, 63, 807-810 (36) Mathies, R.; Oseroff, A.; Stryer, L. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 1-5 (37) White, J. C.; Stryer, L. Anal. Biochem. 1987, 161, 442-452 (38) Larson, A. P.; Ahlberg, H.; Folestad, S. Appl. Opt. 1993, 32, 794-798
Figure 4. Theoretical photodestruction curve for IR 140 (s) with empirically determined values (O) using the two-channel photobleaching technique.
was constructed using the following equation
S′ )
1 F
xπ2 ∫
1
0
1 - exp(- x2Fu) du 2u x-log u
(3)
where S′ is the normalized fluorescence intensity, F is the photoalteration constant, and u is an integration variable. To obtain the photoalteration constant, the focused laser beam radius (ω), the laser power (P), and the molar absorptivity () and quantum yield of photodestruction (Qd) of the molecule must be known. The photoalteration constant is given by the relationship
F)
3.8 × 10-21 ∈ PQd
xπωv
(4)
where v is the linear velocity of the fluorophore. Lee determined the quantum yield of photodestruction to be 2.6 × 10-6 for IR140.39 By calculating the photoalteration constant at various velocities and plugging them into eq 3, the curve represented in Figure 4 is obtained. By normalizing the fluorescence signal obtained in the twochannel measurements at various flow rates, the empirical data were placed on the photodestruction curve shown in Figure 4. As can be seen, a close match was obtained between the calculated and theoretical curves. Discrepancies from the theoretical curve could be attributed to optical saturation of the fluorescence transitions by the laser and the photobleaching that occurred in the second probe region. Therefore, from this model, the average linear velocity of the solution could be obtained by simply measuring the amount of photobleaching in the first channel. This (39) Lee, Y. H. Ph.D. Dissertation, University of Florida, Gainesville, FL, 1995.
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Table 1. Parameters Used for Individual and Sequential SMM parameter
value
IR 140 concentration laser power (beam 1 ) beam 2) estimated probe volume average linear flow velocity calculated transit time
9 µm i.d., 150 µm o.d. fused silica 0.1 pM 20 mW 0.64 pL 1.21 cm/s 0.58 ms
capillary
allowed accurate measurement of the average velocity needed as a benchmark for the two-channel studies with no modifications to the SMD apparatus. Channel Characterizations and SMM. Before sequential single molecule measurements were made, each detection channel was characterized individually to validate single-molecule sensitivity. The methodology established by Soper et al.40 to confirm single-molecule detection was used to perform these studies. Two indirect methods of single-molecule detection include (1) higher signal counts per transit time for the analyte than the blank in the histograms of the data stream and (2) autocorrelation of the data, yielding a nonrandom correlation peak with a width corresponding to the molecular transit time through the laser beam. Direct confirmation of SMD is accomplished by the observation of fluorescence bursts from individual molecules. Adding to this list of requirements to validate single-molecule sensitivity, this study included a higher level of confirmation through the detection of a single molecule sequentially in two probe regions. Table 1 gives the experimental parameters used in both the individual and dual channel studies. The probe volume was defined by the intersection of the capillary inner diameter and the beam waist, of the focused laser. By using a laser beam waist which was slightly larger than the inner diameter of the capillary, the flowing analyte stream was completely interrogated with the excitation source, yielding a highly efficient spatial probing efficiency (s ) 1). Calculation of the probe volume was done in the same manner as in previous work.14 Improvements of focusing optics and a smaller inner diameter capillary have decreased the probe volume from 1 to 0.64 pL. This decrease allowed the use of lower laser powers while an equivalent power density (19.6 kW/ cm2) was maintained. The residence time of the molecule in the probe volume was calculated14,20 to be 0.58 ms using the beam waist size (9 µm) and the average linear velocity (1.21 cm/s) obtained in the foregoing flow studies. The probability of multiple occupancy in the probe volume over the transit time was calculated using a Poisson distribution.14 At a 0.1 pM concentration, the probability of molecular occupation within the probe is 0.962, 0.037, and 0.0007 for zero, one, and two molecules, respectively. Thus, the chance for multiple occupancy was considered to be insignificant for these studies. Histograms, autocorrelations, and photon burst observations confirmed that single-molecule sensitivity was accomplished. Histograms of the raw data made for both channels revealed that there were many more counts per integration time (200 µs) in the analyte signal than in the blank. This gave some preliminary indirect data showing single-molecule sensitivity. Autocorrelation (40) Soper, S. A.; Shera, E. B.; Martin, J. C.; Jett, J. H.; Hahn, J. H.; Nutter, H. L.; Keller, R. A. Anal. Chem. 1991, 63, 432-437.
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Figure 5. Autocorrelation traces for blank and IR140 for both channels. Calculated molecular transit time is 0.58 ms.
analysis is another method typically used to gain information about the detection of single fluorophores and is given by13
G(τ) )
1 N-1
∑ h(t)h(t + τ)
N t)0
(5)
where G(τ) is the value of the autocorrelation function, h(t) is the data point at time t, and h(t + τ) is the data point at time t + τ. A peak in the autocorrelation function results from a nonrandom event occurring such as a correlated burst of photons from a single molecule as it traverses the laser probe region. The width of the nonrandom peak gives information about the average transit time of the molecule through the probe region. Autocorrelation analysis was done for the data from each channel and is shown in Figure 5. As can be seen, the blank in each channel shows no correlation and IR140 shows the nonrandom correlation feature indicating single molecule sensitivity. The lower peak height in the channel 2 correlation shows that channel 1 is more sensitive. Furthermore, each detection channel yielded a nonrandom peak with a width of ∼0.6 ms which agreed very well with the estimated molecular transit time value of 0.58 ms. An autocorrelation peak corresponding to the molecular transit time and higher counts in the 0.1 pM IR 140 raw data over the blank provide indirect proof of the detection of single molecules. Featureless autocorrelation traces of the blanks show that the measurements have a low-level random background, i.e., shot noise limited. Modest signal-to-noise ratios obtained in the raw data precluded efficient assignment of individual molecular bursts. Therefore, as with many SMD techniques, the raw data were processed using a digital summing filter to selectively enhance the photon
Table 2. Results from Independent Channel Characterizations parameter
channel 1
channel 2
expected number of molecules measured number of events detection efficiencya laser probing efficiency sample transport efficiency overall measurement efficiency av number of photoelectrons per moleculeb av number of background counts/transit time average S/Nc
54 53 0.98 ∼1 ∼1 0.98 9
54 52 0.96 ∼1 ∼1 0.96 8
0.29
0.26
30.7
30.5
a Ratio of number of measured molecules to number of expected molecules. b Calculated with (∑C)/n, where n is the number of molecules measured in the measurement time above the discriminator and c is the average number of photon counts from an individual molecule using the raw data. c Ratio of average photoelectrons/ molecule to average background counts per transit time.
Figure 6. Independent signals for channels 1 and 2 processed using a quadratic summing filter revealing bursts from individual molecules. The dotted line represents the discriminator level.
burst signal over the background. This is typically done using a weighted quadratic summing filter given by k-1
S(t) )
∑w(t) d(t + τ)
2
(6)
obtained for channel 1, both laser beams were interrogating the capillary simultaneously, while for channel 2, laser beam 1 was blocked. Therefore, the increased amount of photons reaching detector 1 could have originated from molecules excited in probe region 2 and propagated down the capillary to the first probe region. Analyte signals obtained in later experiments at greater interprobe volume distances demonstrated a decreased number of counts under the discriminator with no change in the blank signals. Table 2 summarizes the results from the experiments in which each channel was characterized individually. The number of molecules expected to pass through the probe volume (Ne) over the measurement time (T ) 800 ms) is given by
τ)0
Nm ) 〈Np〉T/τ where w(t) is a weighting factor, d(t + τ) is a raw data point at time t + τ, τ is a delay time usually set to the transit time of the molecule, and k is the number of integration bins per transit time. The weighting factor describes the shape (distribution) of the photon burst as each molecule traverses the laser beam. Gaussian, triangular, square, and ramp functions have been used for this factor. Statistical simulations were performed in collaboration with the University of Florida Department of Statistics and revealed that the best sensitivity enhancement was achieved using a weighting function of w(t) ) 1.41 Given the transit time of 0.58 ms and the integration bin size of 0.2 ms, there were three bins per transit time (k ) 3). Figure 6 shows the raw data processed with the quadratic summing filter with a weighting function equal to 1. After being passed through the summing filter, photon bursts from individual molecules are clearly visible in the 0.1 pM IR140 data stream while the blank shows only random low-level fluctuation. To minimize the false positive probability of detecting single molecules, the discriminator was set to a level above which no blank signal was detected [S(t) ) 5]. Each peak detected above the discriminator level was then assigned to be a singlemolecule event. It was observed that the number of counts below the discriminator was higher in the IR140 signals than in the blank; especially in channel 1. This was attributed to fluorescence crosstalk between channel 2 and channel 1. When data were (41) Teng, C.-H. personal communication.
(7)
where Np is the average number of molecules in the probe volume over the transit time (τ). At a concentration of 0.1 pM IR 140, a linear flow velocity of 1.2 cm/s, and a probe volume of 0.64 pL 〈Np〉 ) 0.039 and Nm ) 54 molecules. An average total of 53 and 52 molecules in channels 1 and 2, respectively, was detected, yielding average detection efficiencies near unity (0.98 and 0.96, respectively). As indicated by the average number of photoelectrons per molecule, channel 1 was slightly more sensitive (9.6 pe/molecule) than channel 2 (8.3 pe/molecule). This was attributed to the higher peak transmission of the channel 1 fluorescence interference filter (∼45%) compared with the one in channel 2 (∼30%). Differences between expected and measured number of molecules could be explained by shot noise limited sampling statistics, errors in the dilution, and photobleaching of some molecules prior to analysis. Limits of detection in single-molecule detection have been theoretically described by Stevenson and Winefordner in terms of error rates and photocount probabilities.20-22 In that work, they showed that the limit of guarantee (LOG), a more conservative estimate of limit of detection (LOD), must be attained in order reach a detection efficiency of unity. At the LOD, there is a probability of ∼0.02 of a false positive error (R) and a 0.05 probability of a false negative error (β). Being a more conservative estimate, the LOG describes a signal level which offers R and β Analytical Chemistry, Vol. 69, No. 13, July 1, 1997
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errors of e0.0014. At the LOD, the molecule will be detected at a 95% confidence level (β error limited) and a 99.86% detection confidence at the LOG. At the average background rate in this work (respective rates of 0.29 and 0.26 counts/transit for channels 1 and 2), the average number of photocounts per molecule needed to reach the LOG would be 12.7 counts/molecule and only 4 counts/molecule for LOD. Both channels had average photocounts per molecule above the LOD but fell short of the LOG level. Thus, molecules were counted above a 95% confidence level, but they were below 99.86%. Since the discriminator level in these studies was chosen in order to completely eliminate false positive errors (R), the limitation in the detection efficiency was due to false negative events. This was evident in the lower number of molecules detected as compared to the expected number calculated. Moreover, the fact that the detection efficiencies lie between 0.98 and 0.96 validates that the observed photon bursts are detected between the LOD and LOG. Given that the sample transfer (T ) and laser probing efficiencies (p) were both near unity, the overall measurement efficiency (m) for channels 1 and 2 were 0.98 and 0.96, respectively. Thus, by the definition set forth in eq 1, it can be stated that individual molecules in the sample are being measured (or counted) and not just detected. Despite the moderate signal-tonoise ratio afforded by this technique, very high measurement efficiencies are obtained due to the efficient interrogation and imaging of the sample stream within the capillary. Furthermore, this SMM method is amenable to many microchemical techniques because a microcapillary is used for the sample flow cell. The next section will describe measuring molecules sequentially as they pass through two probe regions. Sequential SMM. Measuring molecules in sequential probe volumes further confirms the detection of a single fluorophore. More importantly, sequential detection opens up another dimension of molecular characterization which can be applied in singlemolecule measurement. An important application of two-channel detection is single-molecule electrophoresis.27,28 In this technique, the characteristic electrophoretic mobility of a single molecule is obtained by measuring the time it takes for a molecule to traverse the interprobe volume distance at a given electric field. Despite the significance of this work, only a small portion of the stream was interrogated, thereby precluding accurate counting and efficient quantitation of the sample. Additional studies using this technique could include determining other photophysical properties, such as photobleaching of individual fluorophores. It has been shown in the foregoing section that both channels show the sensitivity necessary to measure single IR 140 molecules using the capillary/MVF technique. Here, both channels are counting simultaneously so that sequential measurement of individual molecules is achieved. Figure 7 shows the signal from both channels acquiring photon counts simultaneously. At an average linear flow velocity of 1.2 cm/s and an interprobe volume distance of 2.784 mm, the average time for a molecule to traverse the distance is 232 ms. In Figure 7, channel 2 was aligned with channel 1, with a delay time matching the average interprobe volume travel time, to show sequential single-molecule peaks. As can be seen, the positions of the numbered peaks match up quite well, indicating that molecules were being measured sequentially. Numbers with arrows underneath them in channel 2 in Figure 7 represent areas where a photon burst is expected, but the signal is not above the discriminator level. This could have been due 2432
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Figure 7. WQS sequential single-molecule data with channel 2 delayed by 230 ms. Peak 7 in channel 2 is denoted with an arrow to show no observed signal above discriminator as expected.
to either photobleaching of the molecule in the first probe region or a false negative detection of the molecule. Since the measurement efficiency of the second channel was found to be 96% in the previous experiments, it was concluded that most of the undetected molecules in the second channel were photobleached. Further confirmation was shown by calculating the percentage of molecules photobleached by taking the ratio of the number of molecules counted in the second probe volume to the number counted in the first. The average extent of photobleaching was calculated to be 42%, which agrees very well with the value of 39% interpolated at 1.2 cm/s from the calculated photodestruction curve depicted in Figure 4. This result further illustrates the high measurement efficiency of the presented technique. The calculated average delay time in molecular arrival from channel 1 to channel 2 was 229.5 ( 5.2 ms, which correlates well with the estimated 232 ms time calculated using the average flow rate and interprobe volume distance. The significant time deviation in the measured peak arrival time is attributed to the differences in linear velocity across the parabolic flow profile within the capillary. Cross-correlation is a powerful tool to determine the similarity of two signals obtained from different wave functions. By multiplying the two time-varying wave forms together and integrating over all time, the cross-correlation of the waves is calculated. This is given by
∫
1 T f1(t)f2(t Tf∞2T T
C1,2(τ) ) lim
- τ) dt
(8)
where τ is the delay time between the two functions and C1,2 is
Figure 8. Cross-correlation of single-molecule data recorded independently in two channels. Calculated interprobe volume travel time is 232 ms.
the cross-correlation of the two functions f1 and f2.42 The correlation value will be highest when both functions are most similar at a given delay time. This type of analysis is useful for two-channel SMM because it will reveal a peak at the time for the molecule to cross the interprobe volume distance provided that the fluorescence bursts are truly due to identical single molecules. A cross-correlation analysis (Figure 8) was performed using commercially available software. A significant peak is (42) Hieftje, G. M.; Haugen, G. R. Anal. Chem. 1981, 53, 755A-766A.
centered at ∼230 ms, which agrees very well with the calculated interprobe volume travel time of 232 ms. This shows that the signals from the individual molecules are being detected in a sequential manner with a delay time correlating to the measured average linear flow rate and the distance between the probe volumes. The width of the peak is determined by molecular diffusion and differing velocities of molecules which depend upon their position within the parabolic flow profile. However, diffusion calculations have shown that the peak width of the crosscorrelation is dominated by the flow profile and not by diffusion. A simple method to decrease the peak width would be to initiate flow through the capillary by electroosmosis, which has a plugtype profile. In this case, not only would molecular travel be less variable but the molecules could be identified on the basis of their electrophoretic mobility.27,28 ACKNOWLEDGMENT The authors thank Chi-Hse Teng and Professor Mark Yang of the University of Florida Department of Statistics for all of their help in describing and modeling many phenomena we encountered with the detection of single molecules.
Received for review November 22, 1996. Accepted April 23, 1997.X AC9611879 X
Abstract published in Advance ACS Abstracts, June 1, 1997.
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