Anal. Chem. 2001, 73, 5030-5037
Quantitative Dosing of Surfaces with Fluorescent Molecules: Characterization of Fractional Monolayer Coverages by Counting Single Molecules David C. Hanley and Joel M. Harris*
Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850
Quantitative deposition of dye molecules onto a substrate has been achieved at very low surface concentrations, in the range of 5 × 10-8-1 × 10-6 monolayer, using the technique of controlled substrate withdrawal from solution. These small surface populations were determined with high (g96%) efficiency by single-molecule counting using an epi-illumination, fluorescence microscope with charge-coupled device detector. The fluorescence imaging resolution (3σ) is 0.78 µm; over a uniform excitation area of 67 × 67 µm2, a large number (>7500) of spatially resolved channels are available for counting individual molecules. At low coverages, the number density of fluorescence spots on the surface agrees with the expected surface concentration of molecules, based on the concentration of dye in solution and the solution film thickness predicted from theory. When the surface density of molecules is high enough that fluorescence spot overlap is likely to occur within the optical resolution of the instrument, the observed fewer number of spots can be corrected for overlap through a site occupation model based on Poisson statistics. Detection of single molecules on surfaces by fluorescence microscopy1,2 is becoming a useful analytical tool for characterizing adsorption and mobility of molecules at or near surfaces,3-6 for imaging properties of inhomogeneous materials,7,8 and for studying analyte binding or recognition by immobilized biological molecules.9-12 While these investigations have produced spectacular results in terms of characterizing small populations of (1) Trautman, J. K.; Macklin, J. J. Chem. Phys. 1996, 205, 221-229. (2) Xie, X. S.; Trautman, J. K. Annu. Rev. Phys. Chem. 1998, 49, 441-480. (3) Schmidt, Th.; Schultz, G. J.; Baumgartner, W.; Guber, H. J.; Schindler, H. J. Phys. Chem. 1996, 99, 17662-17668. (4) Xu, X.-H. N.; Yeung, E. S. Science 1998, 281, 1650-1653. (5) Wirth, M. J.; Swinton, D. J. Anal. Chem. 1998, 70, 5264-5271. (6) Wirth, M. J.; Swinton, D. J. J. Phys. Chem. B 2001, 105, 1472-1477. (7) Hou, Y.; Bardo, A. M.; Martinez, C.; Higgins, D. A. J. Phys. Chem. B 2000, 104, 212-219. (8) Mei, E.; Bardo, A. M.; Collinson, M. M.; Higgins, D. A. J. Phys. Chem. B 2000, 104, 9973-9980. (9) Castro, A.; Williams, J. G. K. Anal. Chem. 1997, 69, 3915-3920. (10) Loescher, F.; Boehme, S.; Martin, J.; Seeger, S. Anal. Chem. 1998, 70, 3202-3205. (11) Taylor, J. R.; Fang, M. M.; Nie, S. Anal. Chem. 2000, 72, 1979-1986. (12) Trabesinger, W.; Hecht, B.; Wild, U. P.; Schu ¨ tz, G. J.; Schindler, H.; Schmidt, Th. Anal. Chem. 2001, 73, 1100-1105.
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molecules, quantitative interpretation of the results in these experiments has been limited to conclusions about the relative fractions of molecules on the surface occupying different binding or adsorption sites. The results have not been interpreted on an absolute quantitative basis due to the significant challenge of preparing standards of known surface concentration. In this study, we test the feasibility of quantitative deposition of molecules at very small fractional monolayer coverages onto surfaces by withdrawing the substrate from a solution of known concentration.13-18 Unlike Langmuir-Blodgett film transfer, where density of molecules on a surface is controlled by film pressure and relative concentration at the air-water interface (which is then transferred to a solid substrate), the substrate-withdrawal technique does not require that the analyte be amphiphilic with low water solubility so that it accumulates at an air-water interface. Substrate withdrawal is analogous to spin coating, except that centripetal acceleration is replaced by a gravitational field allowing solutions of much lower viscosity to be deposited onto surfaces as uniform films. Substrate withdrawal was first applied to deposition of very thin (10 nm-1 µm) polymer layers onto glass and Mylar substrates.13 The method has also been used to vary the surface concentration of dye molecules on silica surfaces to observe coverage effects on optical absorption and fluorescence yields of adsorbed dye14 and, at a fixed concentration of dye, to study molecular orientation on quartz surfaces using reflection and transmission UV-visible spectroscopy.15 Substrate withdrawal has further been applied to dosing of fixed concentrations of an adsorbate onto metal-island films to investigate the enhancement of surface-enhanced resonance Raman scattering (SERS), and surface-enhanced fluorescence.16,17 Recently, the quantitative control capabilities of the substrate-withdrawal method were tested for dosing of small molecules onto glass surfaces from solution.18 The technique was evaluated by measuring ex situ fluorescence from dye molecules rinsed from the surface on which they were (13) Yang, C.-C.; Josefowicz, J. Y.; Alexandru, L. Thin Solid Films 1980, 74, 117-127. (14) Garoff, S.; Stephens, R. B.; Hanson, C. D.; Sorenson, G. K. Opt. Commun. 1982, 41, 257-262. (15) Elking, M. D.; He, G.; Xu, Z. J. Chem. Phys. 1996, 105, 6565-6573. (16) Weitz, D. A.; Garoff, S.; Gersten, J. I.; Nitzan, A. J. Chem. Phys. 1983, 78, 5324-5338. (17) Schlegel, V.; Cotton, T. M. Anal. Chem. 1991, 63, 241-247. (18) Lacy, W. B.; Olson, L. G.; Harris, J. M. Anal. Chem. 1999, 71, 2564-2570. 10.1021/ac010572h CCC: $20.00
© 2001 American Chemical Society Published on Web 09/21/2001
Figure 1. Schematic of the fluorescence imaging instrument. (A) a 514.5-nm band-pass filter, (B) is a 525-nm dichroic beam splitter, (C) is the 100× microscope objective, (D) is a 530-nm, high-pass emission filter, and (E) is a prism that directs the light to the CCD detector. See text for details.
deposited; controlled deposition of surface concentrations was demonstrated in the range of 2%-30% of a monolayer, which could be varied by changing the withdrawal rate and concentration of dye in solution. Controlled variation of surface concentrations was then employed in determining the surface coverage dependence of SERS intensity from SiO2-overcoated silver island films.18 In the present study, we employ substrate-withdrawal quantitative deposition of dye molecules on a substrate at much lower surface concentrations, in the range of 5 × 10-8-1 × 10-6 monolayer. The concentrations of these small surface populations are determined by single-molecule counting using a laser excitation epi-illumination inverted fluorescence microscope with cooled, charge-coupled device (CCD) detector. The fluorescence imaging resolution (3σ) of the scope is 0.78 µm, and the excitation is uniform within 5% over an area as large 67 × 67 µm2, which provides a large number (>7500) of resolved spatial channels within which to count individual molecules. At lower molecular coverages, the number density of fluorescence spots on the surface agrees, within the counting statistics, with the expected surface concentration of molecules, based on the concentration of dye in solution and the solution film thickness predicted from the substrate-withdrawal rate and the viscosity, density, and surface tension of the solvent. When the surface densities of molecules are high enough that fluorescence spot overlap within the optical resolution of the instrument becomes probable, the observed number of spots can be corrected for overlap through a site occupation model based on Poisson statistics. EXPERIMENTAL SECTION Sample Preparation. Solutions of rhodamine-6G (Exciton, Inc. rhodamine 590 chloride) in methanol were prepared at concentrations of 2.0 × 10-11, 5.0 × 10-11, 1.0 × 10-10, 2.0 × 10-10, and 4.0 × 10-10 M by serial dilution. Solution films containing the various concentrations of dye were deposited onto glass substrates (VWR 24 × 40 mm No. 1 microscope cover slips) by lowering the solution away from the fixed substrate, using an
apparatus manufactured in-house from a Velmex UniSlide platform mounted vertically on an angle bracket and driven by a Pittman stepper motor.18 The platform, which supports a beaker containing the dye solution, is first raised until the solution covers the solid substrate, which is held above by a clamp. The platform is then immediately lowered until the surface of the solution drops below the bottom edge of the substrate, leaving a thin solution film on its surface. After the solvent has evaporated, the substrate is removed, and one side of the cover slip that will be in contact with the immersion oil of the microscope objective is cleaned repeatedly by swabbing with methanol. Fluorescence Microscopy. The schematic of the fluorescence microscope is shown in Figure 1. The excitation source is a Spectra-Physics model 165 argon ion laser operated at 514.5 nm. The laser beam is shuttered under computer control with a Uniblitz electronic shutter to allow the CCD to read the charge off the chip without continued accumulation of signal during charge transfer. The excitation beam passes through a PellinBroca prism and aperture to block plasma lines. The beam then impinges on a rotating, roughened glass disk that serves to create an incoherent spot for excitation. The disk is rotated at several hundred revolutions per minute to average the speckle pattern on the time scale of the experiment. The spot source is reimaged using a 55-mm focal length, f/1.2 camera lens (Canon) into the back of the microscope in order to overfill the collection cone of the objective, thereby creating a near-uniform excitation field over the observation area of the instrument; the total laser power at the sample is less than 1 mW. The microscope frame is a Nikon Eclipse TE200 inverted stage with coaxial mount control and a filter cube (Chroma Technology Corp.) containing three filter elements. Filter A in Figure 1, is a 514.5-nm band-pass filter with 10-nm bandwidth. After transmission through the band-pass filter, the excitation is reflected by filter B, a 525-nm dichroic beam splitter, into the microscope objective. The objective, “C”, is a Nikon Plan Fluor 100×, 1.3 NA, infinityAnalytical Chemistry, Vol. 73, No. 21, November 1, 2001
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corrected, 0.20-mm working distance, oil immersion lens. The excitation converges at the sample to a 180-µm-diameter spot, producing nearly uniform intensity across about one-fourth of the area projected onto the detector (less than 5% deviation from uniform intensity over half of the image field in both dimensions). Fluorescence collected by the same objective is passed through the dichroic beam splitter, and through a 530-nm, high-pass emission filter (“D”). The fluorescence is then redirected by a prism, “E”, to the detector. The CCD detector (Andor) contains an antireflection-coated, 1024 × 1024 pixel, back-thinned EEV chip with 13-µm square pixels. The area of the CCD chip (1.77 cm2) corresponds to a detection area at the sample surface of 1.77 × 104 µm2. Images from the central 512 × 512 pixel area of the chip are collected (10-s integration) and stored. Data were processed within 75 by 75 pixel subplots, each corresponding to an area of 95 µm2. The data from 10 subplots, selected randomly from each image were analyzed; for each sample, five or six images were analyzed corresponding to 50-60 subplot areas. Image processing was carried out in Matlab (Mathworks). The subplot images were Fourier filtered to eliminate the dc offset and the single lowest spatial frequency. This provided a flat, meancentered background on which to count fluorescence spots. Fluorescence spots above the background were counted manually on contour plots, using an intensity threshold that was g4 times the standard deviation of the background noise, making the false positive error rate negligible (1.0 cm/s) corresponding to thicker solution films, the surface coverages observed in fluorescence microscopy images were not uniform. The reason for this difference could be detected visually as the solvent evaporated. Thin solution films could be seen to dry quickly in a sheet, while for thick solution films, the slower evaporation of excess solvent resulted in beading and the formation of regions of higher and lower molecular density. Repeated quantitative measurements on surfaces dosed with thicker solution films converged toward the theoretical prediction of eq 2, but with excess variance beyond Poisson statistics due to the inhomogeneity of the film-drying process. The inhomogeneity of dosing with thicker solution films was not reported in a previous quantitative study of substrate withdrawal;18 in the previous study, large areas (>0.1 cm2) of the surface were interrogated which would have averaged the inhomogeneity in surface coverage. To test the surface-dosing procedure and the efficiency of counting deposited fluorescent molecules on the glass surface, substrates were dosed from a series of low concentration dye solutions (2.0 × 10-11-4.0 × 10-10 M) at a fixed withdrawal velocity (0.5 cm/s) and then examined by fluorescence microscopy. The fluorescence images show readily detectable spots having a radius of ∼0.3 µm, which is close to the theoretical resolution limit of 0.26 µm for the 1.3 NA microscope objective. An example image is plotted in Figure 3. The number of intensity spots within the 75 × 75 pixel (9.75 × 9.75 µm) image frames are counted by setting a threshold in the data at a level of 4 times the standard deviation of the background noise. This decision level makes the probability of simple background fluctuations rising above the threshold less than 3 × 10-5/pixel or less than 0.17 in any frame. Blank slides were also imaged and counted, and the number of spots found in 60 blank frames averaged 2.0/frame, with a frame-to-frame standard deviation of 2.4 counts. This level of surface contamination by fluorescent molecules or submicrometer particles is quite low, 2.1 × 106 cm-2, but its magnitude and variation influence the counting of spots at the lowest surfacedosing levels (see below). For dosing at each solution concentration, 50 frames on average, from several slides, were counted, converted to spot densities, and listed in Table 1. At lower molecular surface coverages (up through a coverage of 2.7 × 107 cm-2), the observed density of fluorescence spots agrees with the expected numbers of molecules dosed onto the surface (plus the background) within the reproducibility of counting the spots; see Figure 4. This result indicates that the dosing procedure is accurate for generating a standard surface concentration of molecules at coverages as low as 5 × 106 cm-2 or ∼5 × 10-8 of a monolayer. The results also show that the efficiency of counting single rhodamine-6G molecules at the glass-air interface is very high, g96%, based on the slightly lower density of counted spots compared to the expected molecular surface concentration at the lowest three coverages. The detection efficiency is not surprising since the oil immersion (1.3 NA) objective of the fluorescence microscope
Figure 3. (top) Three-dimensional projection and (bottom) contour plot of the fluorescence from a glass substrate having a rhodamine6G coverage of 5.3 × 105 molecules/cm2. Deposition conditions are 0.5 cm/s substrate withdrawal from a 2 × 10-11 M solution of rhodamine-6G in methanol. The z-axis scale is intensity in units of the A/D converter charge resolution (ADUs) from the CCD, where 1 ADU ≈ 10 photoelectrons.
provides a high (>40%) collection efficiency and the backilluminated CCD detector exhibits a near-unity (>90%) photoelectron quantum yield. These efficiencies combine to produce singlemolecule peaks with maximum intensities that average 19 000 photoelectrons, which are easily resolved from the substrate baseline noise that exhibits a standard deviation of 900 photoelectrons (see Figure 3). Quantitation at Higher Surface Coverages. As presented above, the fluorescence images of lower molecular coverages yielded fluorescence spot counts in good agreement with the expected number of molecules derived from the predictions of controlled-withdrawal dosing. The spot densities at higher coverages, however, fall below the predicted molecular coverages by a significant fraction that exceeds the uncertainty in the results (see the highest concentration entries in Table 1). The reason for this discrepancy can be readily observed in a fluorescence image of a higher coverage sample, as shown in Figure 5. At molecular coverages exceeding ∼3 × 107 cm-2, the average distances between fluorescence spots begins to approach the optical resolution limit of the microscope, and overlap of fluorescence spots reduces the number of resolved spots compared to the number of molecules on the surface. Note that the convergence of spots at higher coverages is not due to molecular association,12 since the average distance between molecules remains large relative to the molecular scale, ∼1.0 µm Analytical Chemistry, Vol. 73, No. 21, November 1, 2001
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Table 1. Test of Quantitative Surface Dosing by Single-Molecule Counting dosinga solution concn, M
expectedb molecular surface coverage, cm-2
molecular coverage plus background, cm-2
measured spot density,c cm-2
predicted Poissond spot density, cm-2
2.0 × 10-11 5.0 × 10-11 1.0 × 10-10 2.0 × 10-10 4.0 × 10-10
5.26 × 106 1.33 × 107 2.65 × 107 5.30 × 107 1.06 × 108
7.40 × 106 1.54 × 107 2.86 × 107 5.51 × 107 1.08 × 108
7.07 ((1.0) × 106 1.45 ((0.19) × 107 2.76 ((0.17) × 107 4.97 ((0.19) × 107 8.04 ((0.35) × 107
7.25 × 106 1.47 × 107 2.64 × 107 4.74 × 107 8.12 × 107
a Substrates dosed with R6G in methanol at a fixed withdrawal velocity, U ) 0.50 cm/s. b Molecular surface coverage based on eq 2. c Results are an average 50 frames for each, includes background spot counts; uncertainties are 95% confidence bounds on the average. d Predicted numbers of counted peaks based on a Poisson overlap model, eq 10, where Nc ) 1.7 × 108 ( 0.2 cm-2.
Figure 4. Resolved fluorescence peaks per unit area versus expected molecular coverage of rhodamine-6G. Data points (with (2σ error bars) are the spot counts for substrates withdrawn at 0.5 cm/s from methanol solutions containing from 2.0 × 10-11 to 4.0 × 10-10 M rhodamine-6G. Dashed line has a slope of 1.0 and an intercept (determined from blank measurements) of 2.1 × 106 cm-2; full line is the least-squares best fit to eq 10 for Nc ) 1.8 × 108 ( 0.2 cm-2.
at the highest coverage. While these coverages do not allow optical resolution of all the molecules on the surface, the onset of dimerization occurs at far higher surface concentrations. It has been shown that dimerization of adsorbed rhodamine-6G on silica xerogels at full monolayer coverages gives rise to significant changes in the electronic absorption spectrum of the dye including band shifting and broadening.21 At coverages as high as 0.3 monolayer on a glass surface, however, 5 orders of magnitude higher than the highest coverage used in these experiments, no shift in the absorption spectrum of rhodamine-6G is observed.18 To account for the loss of fluorescence spots due to overlap, we develop a model to predict the fraction of molecules that falls within the limiting optical resolution of the microscope as a function of the coverage. If the small numbers of molecules on the surface are drawn with low probability from a much larger population in solution and dispersed randomly over the surface, then the occupancy of sites on the surface and the likelihood of molecular overlap should follow Poisson statistics.22 Poisson statistics have been used previously to estimate the overlap of chromatographic peaks23 and predict the number of singlets (21) del Monte, F.; Mackenzie, J. D.; Levey, D. Langmuir 2000, 16, 7377-7382. (22) Barlow, R. J. Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences; John Wiley: Chichester, 1989; Chapter 3. (23) Davis, J. M.; Giddings, J. C. Anal. Chem. 1985, 57, 2168-2177.
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Figure 5. (top) Three-dimensional projection and (bottom) contour plot of the fluorescence from a glass substrate having an expected rhodamine-6G coverage of 1.06 × 108 molecules/cm2. Deposition conditions are 0.5 cm/s substrate withdrawal from a 4.0 × 10-10 M solution of rhodamine-6G in methanol. The z-axis scale is in ADUs, where 1 ADU ≈ 10 photoelectrons.
(isolated peaks), doublets, triplets, etc., that comprise the observed chromatographic profile. More recently, a Poisson model was used to interpret the saturation counting behavior in fluorescence detection of single molecules eluted by capillary electrophoresis.24 A similar approach is followed here, except that in the present case, we are dealing with molecules randomly distributed on a surface rather than components distributed along a one-dimensional elution axis. Accounting theoretically for overlap between fluorescence spots should extend the range of useful quantitation for single-molecule imaging methods. (24) Chen, D. Y.; Dovichi, N. J. Anal. Chem. 1996, 68, 690-696.
If molecules drawn from a large population in solution are dispersed randomly onto an array of sites on the surface, then the distribution of molecules into those sites should follow a Poisson distribution:
P(r, λ) )
r -λ
λe r!
(3)
where P(r, λ) gives the probability of finding r molecules within a given site and where λ is the expectation or mean value for the number of molecules per site. The size of resolvable sites on the surface depends on the optical resolution of the microscope, corresponding to a limiting area, Ares; if two or more molecules fall within this area, their intensity patterns cannot be distinguished, and they produce a single peak or spot. The probability of finding a single molecule (a singlet) within a given resolved area is given by P(r ) 1, λ); the probability of finding two molecules (a doublet) is P(r ) 2, λ), and so forth. The total number of resolvable sites on the surface, Nc (equivalent to the peak capacity in chromatography), is the total area divided by the limiting resolution: Nc ) Atotal/Ares. The number of peaks, Np, that arise from a given population of molecules on the surface can be determined by adding the probabilities of observing a peak (r g 1) at each of the resolvable sites (i ) 1 to Nc) on the surface: Nc ∞
Np )
∑∑P(r, λ)
If the concentration of molecules on the surface is uniform, then the mean (λ) does not depend on which resolved site is being interrogated (λ is independent of i), so that the summation over i in eq 4 becomes a simple factor, Nc: ∞
∑P(r, λ)
(5)
r)1
The Poisson probability summed from r ) 1 to ∞ gives the fraction of resolved sites that are occupied by one or more molecules. This probability is equivalent to 1 minus the probability that no molecules will be found within a given resolved area, which provides a means of further simplifying the expression:
Np ) Nc[1 - P(r ) 0, λ)] ) Nc[1 - e-λ]
∞
∑
n ) Nc
∞
rλre-λ
r)0
r!
∑
rP(r, λ) ) Nc
r)0
(7)
Dropping the r ) 0 term and removing a factor r gives ∞
n ) Ncλ
λr-1e-λ
∑(r -1!)
) Ncλ
r)0
∞
λr′e-λ
r′)0
r′!
∑
(8)
where r′ ) (r -1). Since the final summation in eq 8 is the total Poisson probability and is equal to unity, the expression for the number of molecules, n, reduces to a simple result:
n ) Ncλ
(9)
where the number of molecules is equal to the number of resolvable sites, Nc, times the mean number of molecules per site, λ, as defined above. To relate this result to the number of observed peaks, eq 9 is substituted into eq 6 to yield
Np ) Nc[1 - e-n/Nc]
(10)
(4)
i)1 r)1
N p ) Nc
molecules that can occupy a given site (r ) 0 to ∞) are multiplied by their corresponding probabilities P(r, λ) and multiplied by the total number of resolvable sites on the surface, Nc:
(6)
where P(r ) 0, λ) ) e-λ is the probability for no molecules being present within a resolved area. Note that this expression is equivalent to a Poisson statistical model developed for interpreting the counting rates of single molecules eluted in capillary electrophoresis,24 where the observed response saturates due to overlap of multiple molecules within the detection volume. While eq 6 predicts the number of peaks given a mean number of molecules, λ, per resolved area, Ares, in practice, Np is observed from a given sample and the desired information is the number of molecules on a surface, n, that produces the observed fluorescence peaks. To determine n, the numbers of possible
It should be noted that spots arising from the background compete for resolved area on the surface with dosed molecules, so that n represents their total number, n ) nb + nm. Equation 10 is fit to the data, where Np is plotted versus n, and Nc is varied to give a least-squares fit. The results are plotted in Figure 4 and listed in Table 1, where Nc ) 1.8(( 0.2) × 108/ cm2; the results show that the Poisson model agrees with the data within the uncertainty of counting the fluorescence peaks. At low molecular coverages, n , Nc, eq 10 converges to a simple equality, n ) Np, which is indeed observed in the low-concentration data where the number of fluorescence peaks is equivalent to the total of the background plus the number of molecules dosed on the surface. The best-fit peak capacity, Nc, determined from the rolloff of the data from a linear dependence, corresponds to a closestpacked hexagonal array of circular spots of radius, r ) 0.40 µm. The distance of critical separation for resolving two peaks is, therefore, 2r ) 0.80 µm, indicating that about a 6-pixel separation between fluorescence peak maximums is sufficient for reliable resolution of their intensity patterns in the images. Twodimensional spatial autocorrelation of a low-coverage image (Figure 6) showed the fluorescence profiles of single molecules were Gaussian, with a standard deviation of 0.26 µm. A resolution factor, Rs ) 0.75 (or 3σ separation),26 is needed for reliable detection of neighboring peaks since this separation produces a 30% saddle between equal-sized peaks and a proportionally smaller saddle as the relative size of the two peaks varies. The size of the single-molecule fluorescence profiles based on this criterion, , (25) Bracewell, R. N. The Fourier Transform and Its Applications; McGraw-Hill: New York, 1978; Chapter 8. (26) Giddings, J. C. Unified Separation Science; John Wiley: New York, 1991; Chapter 5.
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Table 2. Uncertainties in Single-Molecule Counting on a Per-Frame Basis
therefore, predicts a critical separation distance of 3σ ) 0.78 µm. This prediction agrees well with the critical separation distance derived from the peak capacity, Nc, found from the Poisson fit of the numbers of resolved spots versus surface coverage. Therefore, the deviation in the numbers of resolved fluorescence spots from the numbers of molecules on the surface is in quantitative agreement with the observed limiting optical resolution of the microscope. The final issue to be addressed in the present study is the uncertainty in counting fluorescence spots, which places a limit on the quantitative precision of the reported results. Fundamentally, the reproducibility of a quantitative measurement made at the single-molecule level depends on statistical fluctuations of the number of molecules drawn into a sample.24 The counting reproducibility was determined from the frame-to-frame variation in the numbers of fluorescence spots. Over the dosing solution concentration range from 2.0 × 10-11 to 4.0 × 10-10 M, the precision of the counting results was determined for an average of 50 samples at each concentration, where the results are summarized in Table 2. There are two sources of uncertainty in these results: first, the background spot count, nb, which was characterized on surfaces that had not been dosed with dye (see above), averaged 2.0 counts/frame with a standard deviation, σb ) 2.7 counts, which is larger than expected from a Poisson distribution (the source of background count variation may not represent a purely random spatial distribution on the substrate surface on the scale of the image frames). The second source of uncertainty should arise from the variation in the number of molecules sampled, which is predicted by Poisson statistics to be σm2 ) µm. The predicted standard deviation from the sum of the background and molecular variance, σT ) (σb2 + µm)1/2, is compared with observed standard deviation in total spot counts in Table 2. The predicted standard deviations are in good agreement with the observed results, which indicates that the uncertainty in spot counts is governed by the statistical fluctuations in the number of molecules sampled in an image plus the additional variance arising from the spatial distribution of background counts. 5036 Analytical Chemistry, Vol. 73, No. 21, November 1, 2001
std dev
no. of moleculesb
obsdc
predd
total spot countc
prede
2.0 × 5.0 × 10-11 1.0 × 10-10 2.0 × 10-10 4.0 × 10-10
5.0 12.6 25.2 50.4 100.8
6.7 13.8 26.5 47.2 76.4
6.9 14.0 25.1 45.1 77.2
3.8 5.3 5.8 7.3 9.3
3.3 4.3 5.6 7.5 10.3
10-11
Figure 6. Autocorrelation of a 512 × 512 pixel fluorescence image. Substrate was dosed from a 5.0 × 10-11 M solution of rhodamine6G. The autocorrelation averages the images of ∼550 molecules within the 4400 µm2 area. The width of the single-molecule Gaussian response inferred from the 2-D autocorrelation is σx,y ) 0.26 µm. The width of the autocorrelation peak was divided by a factor x2 to obtain this result, to correct for the convolution of the Gaussian response25 that occurs in the autocorrelation step.
spot count
dosinga soln concn, M
a Substrates dosed with R6G in methanol at a fixed withdrawal velocity, U ) 0.50 cm/s. b Molecular coverage from eq 2; frame size is 75 × 75 pixels or 9.75 × 9.75 µm. c Results from an average of 50 frames for each. d Predicted numbers of counted peaks based on a Poisson overlap model, eq 10, where Nc ) 170.6 spots/frame. e Predicted standard deviation in total spot count, based on the sum of the background variance and the Poisson variance from sampling the molecular population (see text).
Summary. Quantitative deposition of dye molecules on a substrate has been achieved at very low surface concentrations, in the range of 5 × 10-8-1 × 10-6 monolayer, using the technique of controlled substrate withdrawal from solution. The concentrations of these small surface populations were determined with high (g96%) efficiency by single-molecule counting using a laser excitation epi-illumination, inverted fluorescence microscope with cooled CCD detector. The fluorescence imaging resolution (3σ) is ∼0.78 µm, and the excitation is uniform within 5% over an area as large 67 × 67 µm2, which provides a large number (>7500) of resolved spatial channels within which to count individual molecules. At low coverages, the number density of fluorescence spots on the surface agrees, within the counting statistics, with the expected surface concentration of molecules based on the concentration of dye in solution and the solution film thickness predicted from the substrate-withdrawal rate and the viscosity, density, and surface tension of the solvent. When the surface densities of molecules are high enough that fluorescence spot overlap within the optical resolution of the instrument becomes probable, the observed number of spots can be corrected for overlap through a site occupation model based on Poisson statistics. The technique of substrate-withdrawal dosing combined with molecular counting by fluorescence imaging microscopy provides a method for quantitative sampling of very low concentrations of dye-labeled molecules in solutions that wet a glass or quartz substrate. Unlike single-molecule detection methods in free solution, observation of sample molecules dosed onto a surface is not limited by diffusion, which can spread the molecules out of the volume of efficient excitation or light collection.27 Through use of microscopic imaging, the detection process is massively parallel and provides a large peak capacity (g7500) in a single 10-s observation; hundreds of such observations can be made on a single substrate by translating the microscope stage. In current work in our laboratory, we are applying the method to determine small numbers of dye labels covalently bound into (27) Demas, J. N.; Wu, M.; Goodwin, P. M.; Affleck, R. L.; Keller, R. A. Appl. Spectrosc. 1998, 52, 755-762. (28) Hanley, D. C.; Harris, J. M. Fluorescence Imaging of Covalently Labeled Silica Nanoparticles: Characterization of Particle Labeling, Distributions, and Chemical Environments. Presented at Particles 2001, Orlando, FL, February 26, 2001; Paper 226.
individual sol-gel particles and the concentration of particles in very low concentration dispersions.28 For this and other labeling applications, the amplitude distribution of single-molecule fluorescence spots plays a critical role in determining the labeling statistics. Analysis of fluorescence intensity distributions from spatially resolved, single molecules deposited onto surfaces at low coverages is also the subject of a current investigation.
ACKNOWLEDGMENT This research was supported in part by the National Science Foundation under Grant CHE-9817934. Received for review May 24, 2001. Accepted August 12, 2001. AC010572H
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