Anal. Chem. 2006, 78, 7707-7715
Determination of the Fraction and Stoichiometry of Femtomolar Levels of Biomolecular Complexes in an Excess of Monomer Using Single-Molecule, Two-Color Coincidence Detection Angel Orte, Richard Clarke, Shankar Balasubramanian, and David Klenerman*
Department of Chemistry, Cambridge University, Lensfield Road, Cambridge, CB2 1EW, UK
We have extended the method of single-molecule fluorescence, two-color coincidence detection (TCCD) to detect coincident events due to a low fraction of a complex against a background of chance coincident events, due to monomers. We developed two complementary methods to determine the number of chance coincident events using the experimental data and without the need for additional experiments. We show that the subtraction of the chance coincidence level is essential for accurate quantification of the relative number of complexes and their stoichiometry. By performing experiments on model samples made from fluorophore-labeled duplex DNA and free dye, a linear dependence on the fraction of duplex DNA was found, independent of the level or ratio of free dye, with quantification down to a level of 0.5% and 500 fM duplex DNA. The method was then used to measure the equilibrium dissociation constant and offrate of a 9-mer duplex DNA, demonstrating the application of this method to systems with nanomolar dissociation constants. These improvements to the method of TCCD analysis significantly extend the application of TCCD to weakly bound complexes and large multicomponent biomolecular systems. Fluorescence analysis of single molecules, one by one, has been developed and applied widely to biomolecules over the past decade both in solution and immobilized to surfaces to probe biomolecular structure, dynamics, and heterogeneity.1-8 Although the observation time is typically less than 1 ms, limiting the time scale of the dynamics that can be probed, experiments in solution have the potential to analyze a large number of molecules without * To whom correspondence should be addressed. E-mail: dk10012@ cam.ac.uk. (1) Xie, X. S.; Trautman, J. K. Annu. Rev. Phys. Chem. 1998, 49, 441-480. (2) Deniz, A. A.; Dahan, M.; Grunwell, J. R.; Ha, T. J.; Faulhaber, A. E.; Chemla, D. S.; Weiss, S.; Schultz, P. G. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 36703675. (3) Weiss, S. Science 1999, 283, 1676-1683. (4) Selvin, P. R. Nat. Struct. Mol. Biol. 2000, 7, 730-734. (5) Greulich, K. O. Chem. Phys. Chem. 2005, 6, 2458-2471. (6) Ha, T.; Rasnik, I.; Cheng, W.; Babcock, H. P.; Gauss, G. H.; Lohman, T. M.; Chu, S. Nature 2002, 419, 638-641. (7) Schuler, B.; Lipman, E. A.; Eaton, W. A. Nature 2002, 419, 743-747. (8) Zhuang, X. W.; Kim, H.; Pereira, M. J. B.; Babcock, H. P.; Walter, N. G.; Chu, S. Science 2002, 296, 1473-1476. 10.1021/ac061122y CCC: $33.50 Published on Web 10/20/2006
© 2006 American Chemical Society
the need for surface attachment, which is potentially perturbative. Solution experiments are normally performed using a tightly focused Gaussian laser beam and confocal detection in order to achieve the smallest possible probe volume. Nevertheless, molecules can take different paths through the laser focus, giving rise to variation in the excitation rate of the fluorophore and hence fluorescence intensity detected. In order to address this issue, ratiometric methods have been developed where two fluorophores are attached to the same biomolecule and the ratio of their fluorescence intensities is measured as they diffuse across the laser-excited volume. If the two fluorophores are sufficiently close and have overlapped emission and absorption spectra, then it is possible to excite the donor fluorophore and get fluorescence resonance energy transfer (FRET) to the acceptor fluorophore so that only one laser is required. Such experiments are performed to measure the conformation of biomolecules since the FRET efficiency depends on the donor-acceptor separation.3 In the more general case, the two fluorophores are independently excited by two different spatially overlapped lasers and coincident fluorescent photons detected as the molecule diffuses across the laser-excited volume. The simultaneous excitation using two different wavelengths was first proposed for fluorescence correlation spectroscopy,9 the so-called dual-color fluorescence cross-correlation spectroscopy (FCCS).10,11 Other methods do not make use of the correlation functions, but rely on coincident events counting and burst selection and have been applied to molecule-by-molecule analysis.12-15 Examples of the latter are the alternating laser excitation (ALEX) and the two-color coincidence detection (TCCD) methods. In the ALEX16 method developed by Weiss and coworkers, the lasers alternate excitation fast enough that a molecule is excited by first one and then the other laser as it diffuses across the confocal volume, while the TCCD method15 is based on (9) Eigen, M.; Rigler, R. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 5740-5747. (10) Schwille, P.; Meyer-Almes, F.; Rigler, R. Biophys. J. 1997, 72, 1878-1886. (11) Kettling, U.; Koltermann, A.; Schwille, P.; Eigen, M. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 1416-1420. (12) Castro, A.; Williams, J. G. K. Anal. Chem. 1997, 69, 3915-3920. (13) Winkler, T.; Kettling, U.; Koltermann, A.; Eigen, M. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 1375-1378. (14) Nolan, R. L.; Cai, H.; Nolan, J. P.; Goodwin, P. M. Anal. Chem. 2003, 75, 6236-6243. (15) Li, H. T.; Ying, L. M.; Green, J. J.; Balasubramanian, S.; Klenerman, D. Anal. Chem. 2003, 75, 1664-1670. (16) Kapanidis, A. N.; Laurence, T. A.; Lee, N. K.; Margeat, E.; Kong, X.; Weiss, S. Acc. Chem. Res. 2005, 38, 523-533.
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Table 1. ssDNA Sequences Used in This Studya
1 2 3b 4 5 a
sequence
label in 5′-end
TAGTGTAACTTAAGCCTAGGATAAGAGCCAGTAATCGGTA TACCGATTACTGGCTCTTATCCTAGGCTTAAGTTACACTA TAGTGTAACTTAAGCCTAGGATAAGAGCCAGTAATCGGTATAGT-GTAACTTAAGCCTAGGATAAGAGCCAGTAATCGGTA TACTGATTA TAATCAGTA
Alexa 488 Atto 647N Alexa 488 Alexa 647 Alexa 488
The 5′ f 3′ sequence is indicated from left to right. b The sequence is split for space reasons.
continuous excitation of the confocal volume by both lasers. Likewise, D’Antoni et al. showed recently the superiority of the coincident events counting approach versus cross-correlation analysis in the quantitation of specific RNA targets by a singlemolecule fluorescence multiple laser excitation instrument.17 All these methods have been used to determine the stoichiometry of molecular complexes or function of biomolecules. For instance, hybridization of complementary DNA strands10 and enzymatic activity of restriction endonuclease EcoRI11 have been studied by means of FCCS; whereas ALEX has been applied to dual-labeled, double-stranded DNA with tags separated by different distances18 or to the interaction of Escherichia coli catabolite activator protein with DNA.19 TCCD has been used to study complexes including (protein G-IgG),20 target DNA sequences,21 and the human telomerase RNA.22 Recently TCCD has been used to study the enzyme activity of human telomerase by analyzing primer extension products with up to five identical fluorophores.23 TCCD has also been shown to be less sensitive to background fluorescence than single-color excitation and capable of detecting femtomolar levels of molecular complex.15 The advantage of excitation of the two fluorophores with two independent lasers is that the fluorophores can be placed at any convenient position on the biomolecule and there is no requirement to place them close for FRET, which may not be possible if there is no information on the structure of the complex. One major problem with single-molecule fluorescence analysis in solution is that it needs to be performed at subnanomolar concentrations, unless special efforts are made to reduce the size of the laser-excited volume. This has important implications in the study of biomolecular complexes: unless the complex that is studied has a subnanomolar dissociation constant, then a significant fraction of the complex may dissociate, so that only a small fraction of the molecules will still be in the complex under the condition of measurement if equilibrium is reached. In studies in which the different components of the complexes are independently labeled, fluorescent events are collected from each com(17) D’Antoni, C. M.; Fuchs, M.; Harris, J. L.; Ko, H.-P.; Meyer, R. E.; Nadel, M. E.; Randall, J. D.; Rooke, J. E.; Nalefski, E. A. Anal. Biochem. 2006, 352, 97-109. (18) Lee, N. K.; Kapanidis, A. N.; Wang, Y.; Michalet, X.; Mukhopadhyay, J.; Ebright, R. H.; Weiss, S. Biophys. J. 2005, 88, 2939-2953. (19) Kapanidis, A. N.; Lee, N. K.; Laurence, T. A.; Doose, S.; Margeat, E.; Weiss, S. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 8936-8941. (20) Li, H.; Zhou, D.; Browne, H.; Balasubramanian, S.; Klenerman, D. Anal. Chem. 2004, 76, 4446-4451. (21) Zhang, C.-Y.; Chao, S.-Y.; Wang, T.-H. Analyst 2005, 130, 483-488. (22) Ren, X.; Gavory, G.; Li, H.; Ying, L.; Klenerman, D.; Balasubramanian, S. Nucleic Acids Res. 2003, 31, 6509-6515. (23) Ren, X.; Li, H.; Clarke, R. W.; Alves, D. A.; Ying, L.; Klenerman, D.; Balasubramanian, S. J. Am. Chem. Soc. 2006, 128, 4992-5000.
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ponent and from the complex itself. The dissociated molecules will give rise to a statistical background level of coincident events, due to stochastic events when two or more molecules with different fluorophores enter the laser-excited volume at the same time. Additional coincident events will also occur when the small fraction of complex enters the probe volume, and so it is important to develop methods to accurately determine the level of the statistical background since this will determine how small a fraction of complex can be detected in addition to the background and what fraction of complex is required in order to determine the complex stoichiometry. The aim of this work was to therefore use model mixtures to first evaluate different approaches and find a better way to determine the statistical background. The method is then used to determine the fraction of complex present with different levels of background and complex to establish whether the method is quantitative and its sensitivity limits. Third, it is extended to determine the complex stoichiometry with different levels of background. Last the method was applied to measure the equilibrium constant and dissociation rate for nine base-pair duplexes of DNA, exploiting its ability to detect down to 0.5% complex in the presence of 99.5% dissociated monomers. MATERIALS AND METHODS Table 1 shows the single-stranded DNA (ssDNA) sequences and the labeling features used in this work. The labeled oligonucleotides were purchased from IBA GmbH and purified by double HPLC. An additional polyacrylamide gel electrophoresis purification step was performed for the 80-mer single strand. Measurements of UV-visible absorbance confirmed the labeling efficiency to be larger than 90% and the absence of free dye. Tris buffer was from USB Co., sodium chloride from Acros Organics, and magnesium chloride from Fluka. All the buffers used were 10 mM in Tris and other components were as follows: TEN buffer, 1 mM EDTA and 100 mM NaCl; TNM1 buffer, 100 mM NaCl and 10 mM MgCl2; TNM2, 300 mM NaCl and 20 mM MgCl2. The free dyes Alexa Fluor 488 and Alexa Fluor 647 were obtained from Invitrogen. Furthermore, 0.01% Tween 20 was added to all measured samples in order to prevent surface adsorption of the molecules. The annealing of the single strands to form double-stranded DNA (dsDNA) samples was carried out by mixing stoichiometric amounts of each complementary ssDNA, heating to 90 °C, and slowly cooling down to room temperature. In this study, we have used a dual-labeled 40 base-pair (40 bp) duplex (formed by 1 and 2), a dual-labeled 9-bp duplex (prepared with 4 and 5), and 2:1dsDNA model sample by annealing 3 with double the equivalents
of 2, resulting in a dsDNA labeled with one blue fluorophore and two red fluorophores. The apparatus for two-color, single-molecule fluorescence coincidence detection (TCCD) has been reported in detail previously.15 Two Gaussian laser beams (488 nm, argon ion, model 35LAP321-230, Melles Griot and 633 nm, model 25LHP151 HeNe laser, Melles Griot) were overlapped using a dichroic mirror (505DRLP Omega Filters), directed to the back port of an inverted microscope (Nikon Eclipse TE2000-U), and focused 6 µm into 1 mL of sample solution in a Lab-TeK chambered cover glass (Scientific Laboratory Suppliers Ltd., Surrey, UK) by using an oil immersion objective (Apochromat 60×, NA 1.40, Nikon). Fluorescence was collected by the same objective, imaged onto a 50µm pinhole (Melles Griot), and sent to two avalanche photodiodes (APD) (SPCM-AQR-14, Perkin-Elmer Optoelectronics), after the different emissions are separated by another dichroic mirror (585DRLP Omega Filters), and different filters in the blue green (535AF45 and 510ALP Omega Filters) and red channel (696AF55 and 565ALP Omega Filters). The cross-talk (detection of one fluorophore emission in the other channel) for the fluorophores used in this work was calculated by carrying out measurements of free Alexa 488 or Alexa 647 at 100 pM. The cross-talk from the blue channel to the red channel was 1% whereas the cross talk from the red channel to blue channel was negligible. Furthermore, after thresholding, the number of bursts over threshold detected in either channel due to cross talk is negligible. We collected data typically for 90 min, using 8000-division frames with a time binning of 1 ms on both MCS cards. The binning time is long enough to ensure single-molecule bursts are collected in single bins, since the average diffusion time of the DNA through the excitation volume for these experiments is ∼0.3 ms. In order to study the dissociation kinetics of the 9-bp duplex and follow the time course of the measurement, each experiment was analyzed in blocks of 50 frames giving a time resolution of 7 min. This provided a tradeoff between sufficient statistical significance of the measurements and enough time resolution to follow the changes occurring during the DNA dissociation. We used a threshold of 15 counts/ms on both channels to select actual fluorescent bursts. This threshold value is 10-fold higher than the signal from buffer-only measurements. The laser powers were 150 and 80 µW for the blue and red excitation, respectively, except for the 9-bp duplex experiments where the laser powers were 270 and 80 µW, respectively. Due to FRET between the two labels used in the 9-bp duplex, a slightly higher blue laser power was used for better signal-to-noise ratio on the blue channel. All the TCCD measurements were performed at 20 °C, except those experiments to study the dissociation of the 9-bp duplex that were carried out at 8 °C. It has been shown recently that a 488-nm laser can promote an excited red fluorophore to dark states in cyanine dyes, such as Cy5 or Alexa647,24,25 whereas Atto647N showed a higher resistance to these dark pathways.24 We have detected a 30 and 20% decrease in brightness of Alexa 647- and Atto 647N-labeled 40-mer, respectively, at 488-nm laser power of 270 µW. However, under the conditions of our experiments, the decrease in brightness was only ∼6% for Atto647N-labeled 40-mer at 150 µW and (24) Eggeling, C.; Widengren, J.; Brand, L.; Schaffer, J.; Felekyan, S.; Seidel, C. A. M. J. Phys. Chem. A 2006, 110, 2979-2995. (25) Bates, M.; Blosser, T. R.; Zhuang, X. Phys. Rev. Lett. 2005, 94, 108101.
less than 3% at 80 µW. In our experiments, this effect is small and the same for all the red fluorophores, and results in a slightly lower overall value of mean brightness of red fluorophores. Fitting of Logarithmic Ratio Histograms Using Gaussian Distributions. In the TCCD experiments, the parameter of interest is the ratio of fluorescence intensities IR/IB of the coincident events. We used background- and spectral cross talkcorrected intensities, i.e., IB ) SB - BkB, and IR ) SR - BkR RSB, where Si is the total photon count number in channel i, Bki is the average background photocounts acquired from clean buffers in each channel, and R is the spectral cross talk of the blue channel in the red (the cross talk of red photons into the blue channel is negligible). We only select the bursts exceeding a threshold value set according to the background (buffer) levels and mean brightness of the channel. The ratio of fluorescence intensities is a multiplicative parameter, and hence, its distribution is a log-normal function.26 The best way to analyze the intensities ratio distributions is based on fitting the logarithm of ratio of intensities as we have shown previously.23 Recently, Antonik et al. have described the use of uncorrected signal ratio (SR/SB) histograms by means of probability distribution analysis, showing the log-normal distributions of such histograms.27 In our method, the distribution of the function Z ) ln(IR/IB) can be fitted using Gaussian peaks, whose maximum is centered at 〈Z〉 ≈ ln(〈IR〉f/ 〈IB〉f), where 〈I〉f stands for the mean brightness of the fluorophores and the subscripts R and B stand for the red and blue channels, respectively. The width of the Gaussian distribution is assumed to be determined as K1/2 times the shot-noise limit, given by
σ)
x
K K + 〈IR〉f 〈IB〉f
(1)
The value for K is usually determined in independent measurements of model 1:1-dsDNA samples. This allows either fixing or constraining the fitting in unknown samples, decreasing the number of fitting parameters. In cases of 2:1-dsDNA samples, the addition of a second component was justified by more than 20% decrease of the reduced χ2 value in the fitting. For the 2:1 component, the red brightness is given by 2 × 〈IR〉f, which changes the peak center Z and width σ. RESULTS Estimation of the Background due to Chance Coincident Events. The background coincidence level in the TCCD technique is caused by coincident bursts caused by a blue-labeled molecule and an unconnected red-labeled molecule in the excitation volume at the same time. Previous works have not considered how to estimate the statistical background in any detail or have been performed under conditions where the background was negligible.12,19,28-30 More recently, D’Antoni et al. proposed a (26) Limpert, E.; Stahel, W.; Abbt, M. Bioscience 2001, 51, 341-352. (27) Antonik, M.; Felekyan, S.; Gaiduk, A.; Seidel, C. A. M. J. Phys. Chem. B 2006, 110, 6970-6978. (28) Zhang, C.-Y.; Johnson, L. W. Analyst 2006, 131, 484-488. (29) Yeh, H.-C.; Ho, Y.-P.; Shih, I.-M.; Wang, T.-H. Nucleic Acids Res. 2006, 34, e35. (30) Agrawal, A.; Zhang, C.; Byassee, T.; Tripp, R. A.; Nie, S. Anal. Chem. 2006, 78, 1061-1070.
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method to estimate the chance background based on probabilistic calculations.17 This method has been applied by Neely et al. in the determination of microRNAs.31 In this work, we have developed two different methods to estimate the background coincidence caused by chance, the statistical background: a theoretical estimation, and an experimental approach, which were tested using solutions of noninteracting free dyes (Alexa 488 and Alexa 647) at different concentrations. The theoretical prediction of the chance coincident events is based on probabilistic calculations, and it is as follows: A typical TCCD measurement is collected as a series of pairs of frames, each lasting T seconds, divided into many intervals, according to the setup of the multichannel scalar cards. Each interval integrates photons arriving to the detectors during a time t, the time binning. Our measurements were performed using typically 600 frames of 8000 intervals with a time binning of 1 ms. The probability of detecting a burst above threshold in one interval of a channel is therefore given by
P(event) ) Nevents ÷ Nintervals ) Nevents ÷
[Tt] ) r
eventst
(2)
where revents stands for the burst rate. The probability of having bursts simultaneously by chance in both channels in the same time interval is given by the product of the individual probabilities:
P(red)P(blue) ) rRrBt2
(3)
Therefore, the rate of coincident events expected to occur by chance in a particular frame is given by
rE ) Nchance ÷ T ) P(red)P(blue)Nintervals ÷ T
[Tt] ÷ T ) r r t (4)
) rRrBt2
R B
If the entire measurement were to be considered to be a single, extremely long, frame, then this equation would yield an estimate for the overall total number of coincident events due to chance in the measurement. This number of events can be subtracted from the total number of coincident events to determine the number of real coincident events. We do not take into account the very low probability of exciting more than two molecular complexes at the same time since the focus of this work is studies at low concentrations. Equation 4 shows the dependence of the chance coincident events on the product of burst rates in both channels. As the burst rate is proportional to the concentration of fluorophore,9 eq 4 defines a quadratic dependence of the number of chance coincident events with total concentration. This is shown in Figure 1b (red squares). This method is similar to that used by D’Antoni et al.17 However, we use the overall burst probability, whereas D’Antoni et al. used the probability of detecting a burst in one channel with zero photons in the other channel. Moreover, we have found that a more accurate theoretical estimate of the chance coincidence rate can be obtained by summing the expected (31) Neely, L. A.; Patel, S.; Garver, J.; Gallo, M.; Hackett, M.; McLaughlin, S.; Nadel, M.; Harris, J.; Gullans, S.; Rooke, J. Nat. Methods 2006, 3, 41-46.
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Figure 1. (a) Basics of the desynchronization approach to calculate the chance coincident events from the raw TCCD data. (b) Coincident events rates from TCCD measurements of Alexa 488 and Alexa 647 in solution at different concentrations (circles). Rate of coincident events expected to occur by chance, rE (red squares), and calculated by the desynchronized estimator (green squares). This figure shows the excellent agreement between the two methods for background estimation, as well as that the free dyes only showed coincidence due to chance. Data collection over 150 min, using a 1-ms time bin.
number of chance events for each pair of frames, i.e., using eq 4 individually on each frame pair. This second estimator is useful because the burst rates may undergo slight variations with the measurement time, not being homogeneous during the entire measurement. This may be due to factors such as sample evaporation or drift in laser power or optical alignment. The amount that the frame-by-frame estimation exceeds the overall estimation indicates the degree of inhomogeneity of the data and approaches zero for totally homogeneous data. Nevertheless, it should be noted that eq 4 is an approximation, but valid in cases where the rate of coincident events, rC, is much less than rB + rR and rB ≈ rR. In our experiments, this is always fulfilled. The more accurate estimation of rE, as well as typical examples of time drift in burst rate, is detailed in Supporting Information.
We also have developed a second method to estimate experimentally the background coincidence: the desynchronization approach. This approach allows the calculation of chance coincident events by randomly shuffling the frames in one channel and pairing them to the other channel frames (see Figure 1a). The frames in one channel are shuffled randomly in a way that each frame in the blue channel FBi is paired to one frame from the red channel FjR (with j * i). The pairing of desynchronized frames yields the number of coincident events that are purely due to chance coincidence. Basically, the desynchronized pairing mimics a TCCD measurement of noninteracting fluorophores with exactly the same number of bursts and channel brightness as the original measurement, as long as there is low cross talk between both channels, as indeed there is in our experiments. Note that, if it were reasonable in a particular case to assume total homogeneity of the burst rates throughout a set of data, then it would be possible to calculate the chance coincident rate to a high degree of accuracy by averaging over a high number of random pairs of files. However, we have found that it is actually more advantageous not to desynchronize the files randomly and instead to average the two desynchronized combinations of adjacent pairs of files. This ensures that increases in the rate of chance coincidences due to inhomogeneity in the burst rates during the data acquisition are still likely to be cancelled by the desynchronized estimator. The advantage of this approach is that it does not underestimate the number of chance coincidences by falsely assuming total burst homogeneity. These methods thus provide control measurements of the chance background intrinsic to each set of data itself. It is important to note that the desynchronization approach recovers experimental values of intensity in each channel for chance coincident events. Providing that cross talk and FRET are negligible, these events can therefore be used to calculate the expected ratio intensity histograms of chance coincident events. These histograms can then be directly subtracted from the total experimental histogram, allowing us to determine the ratio histogram for the significant coincident events alone. In order to test the validity of both methods, the theoretical prediction and the desynchronization approach, we have compared the chance coincidence levels they predict to those obtained from experimental measurements of free dyes in solution, specifically Alexa 488 and Alexa 647. Figure 1b shows the excellent agreement between the experimental results and the levels of coincidence estimated using both methods. dsDNA in the Presence of Free Dyes. Mimicking Small Fraction of Assembled Dual-Labeled Molecules. An important issue is to determine the detection limits of the technique, i.e., the lowest detectable fraction of assembled dual-labeled molecules in the presence of a majority of single-labeled monomers. To do this we carried out a series of model experiments. Specifically, dual-labeled (5′-Alexa 488 and 5′-Atto 647N) 40-bp dsDNA was dissolved at concentrations between 300 fM and 5 pM in the presence of the free dyes at concentrations between 10 and 100 pM, resulting in percentages of coincident molecules between 1 and 5%. The data were analyzed by first determining the total number of coincident events; the chance coincident events were estimated using both methods above, which gave excellent agreement; the significant coincidence levels were then calculated by subtracting
Figure 2. (a) Linear calibration of the corrected percentage of coincidence vs percentage of dual-labeled DNA. The DNA concentrations were between 300 fM and 5 pM, including a measurement at 30 pM, and free dye concentrations between 10 and 100 pM. Black squares represent experiments with equal concentration of free Alexa 488 and Alexa 647, whereas red circles represent experiments with double concentration of Alexa 488 with respect to Alexa 647. Green triangles represent experiments with dyes only. (b) Linear calibration of the significant burst count rates vs concentration of dual-labeled DNA, from the same measurements of (a). Additionally, blue symbols stand for experiments with dsDNA only, in the absence of free dyes.
the chance coincident events, a crucial step in data analysis. Note that both the statistical background and significant coincidence events are determined in a single experiment without the need to make control samples to measure the background level. In previous works, the parameter used to describe the level of coincidence was the percentage of coincident events (using AND threshold criteria) over the total events (calculated using the OR threshold).15 However, we found the percentage of coincidence to be highly concentration-dependent in the case of low levels of coincidence due to the contribution of chance coincident events. We therefore use instead the background-corrected coincidence percentage, %Ccorr, in which the estimated number of chance Analytical Chemistry, Vol. 78, No. 22, November 15, 2006
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coincident events are subtracted from the total number of coincident events. This parameter is defined as
%Ccorr ) 100% ×
rS rB + rR - rS
(5)
where the significant events burst rate (rS) is given by subtracting the expected coincidence rate due to chance (rE in eq 4) from the total coincident burst rate (rC), and rB and rR stand for the total burst rates in the blue and red channels, respectively. In the denominator, rS is subtracted from rB + rR in order to take into account only the total number of molecules detected, whether they are single- or dual-labeled. Figure 2a shows the linear dependence of %Ccorr versus the percentage of dual-labeled molecules in solution. Note that some measurements were performed with double the concentration of free Alexa 488 compared to free Alexa 647, giving rise to a larger background. Nevertheless, both data sets lie on the same line, showing the statistical background’s contribution has been effectively removed even though it contributed between 50 and 90% of the total coincident events. The corrected coincidence (%Ccorr) plotted versus the percentage of coincident molecules led to a detection limit of 0.54% of coincident molecules, and the quantification limit was 1.78% of coincident molecules (based on IUPAC definitions of detection and quantification limits).32 The TCCD technique is thus able to detect a small fraction of 0.5% of duallabeled complex in the presence of 99.5% of monomeric singlelabeled material. Interestingly, the slope of this calibration was 0.220 ( 0.003, leading to a coincidence detection efficiency of 22.0% for dsDNA only in solution. This is indeed in agreement with the recovered values obtained around 20% in this and previous works.15 Since we know the concentration of DNA used in these experiments, we can also analyze the data to perform a second calibration, the significant coincident burst rates (rS) versus the actual concentration of dual-labeled molecules (Figure 2b). The linear fitting in Figure 2b showed a slope value of 0.126 ( 0.006 pM-1 s-1 and a negligible intercept. This calibration led to a detection limit of 0.5 pM. This graph allows estimation of the actual concentration of dual-labeled molecules from the measured number of significant coincident events. The slope of this linear calibration can be related to the diffusion coefficient. The burst count rate (β) in a single-molecule experiment depends on the concentration (n), the size of excitation volume (radius R0), and the diffusion coefficient (D) by9
β ) 4πR0Dn
(6)
The slope of β versus concentration is 4πR0D. The excitation volume radius in our instrument was calculated by FCS to be 260 nm, yielding a diffusion coefficient of 6.4 × 10-7 cm2 s-1, which is in good agreement with the previously published value for a 40-bp duplex. For instance, the semiempirical equation reported by Stellwagen et al.33 yields a diffusion coefficient of 6.2 × 10-7 cm2 s-1. In order to confirm the concentration independence of %Ccorr, we also performed simulations with synthetic data. Based on burst (32) Spectrochim Acta B 1978, 33, 241-245. (33) Stellwagen, E.; Lu, Y. J.; Stellwagen, N. C. Biochemistry 2003, 42, 1174511750.
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count rates of free fluorophores and significant coincident burst rates of the dsDNA, we have simulated the %Ccorr values in a wider range of cases and shown that the %Ccorr is only sensitive to the percentage of dual-labeled molecules. We have also studied the effect of unbalanced red and blue events by simulating changing the Alexa 647/Alexa 488 ratio from 0.25 to 25. The %Ccorr was found to be insensitive to unbalanced channels. Further details about these simulations can be found in Supporting Information and Figure S-1. Determination of Stoichiometry in the Presence of a Statistical Background. The model systems studied here mimic the situation of a small amount of dual-labeled complex in the presence of a majority of single-labeled monomers. In such situations, the chance coincident events are a major fraction of the total coincident events and make a major contribution to the overall ratio intensity histogram. To remove the contribution of chance events to the histogram, we used the desynchronization approach described above. The corrected histogram, from the real dual-labeled molecules, was obtained by subtracting the average background histogram (from two desynchronizations) from the total histogram as detailed previously. We tested this method using a 2:1-dsDNA model sample with two Alexa-647 fluorophores and one Alexa 488 fluorophore (see Materials and Methods and Table 1), in the presence of free dyes. As an initial test, we tried the 2:1-dsDNA model sample alone in solution. Figure 3a shows an example of recovering the actual histogram (black) after subtraction of the background histogram (cyan) from the total (red). As shown in Figure 3b, the corrected logarithmic ratio histogram was fitted with a Gaussian peak with the ratio of IR/IB centered at {〈IR〉f}/{〈IB〉f} (close to 1 as the laser powers were adjusted to reach similar monomer brightness in both channels) and a Gaussian with the ratio of IR/IB centered at 2 × {〈IR〉f}/{〈IB〉f} (close to 2). A series of experiments carried out with pure 2:1-dsDNA in solution at concentrations between 25 and 50 pM gave the average percentage of the population with a ratio close to 1 as 24 ( 6% and 2 as 76 ( 6%. The presence of the smaller peak centered at a ratio of 1 is caused by either partial dissociation of one strand at low concentrations, hindered hybridization of the second strand, or promotion of dark states in one of the red dyes, which are in different environments. This could not be avoided even by using higher salt in buffers (TNM2 buffer) or lower laser powers. In these cases of pure 2:1-dsDNA, the statistical background, as expected, is small (cyan line in Figure 3a). The same sample was then tested in the presence of a high statistical background from free fluorophores. As in the previous section, we varied the 2:1-dsDNA concentrations between 400 fM and 5 pM in the presence of the free dyes at concentrations between 20 and 100 pM, so that percentages of coincident molecules between 0.8 and 5.0% are obtained and performed each measurement in triplicate. Figure 3c shows as an example the results for a single measurement with a 5 pM solution of 2:1-dsDNA, 45 pM Alexa 488, and 45 pM in Alexa 647, where the statistical background contributes 40% of the total events. The resulting corrected histogram, in Figure 3d, can be fitted as a sum of two Gaussians centered at a ratio of IR/IB of 0.96 and 1.91, respectively, in agreement with the results for the pure 2:1-dsDNA samples. For the series of experiments performed with a high background due to free dye, we also found that we could recover
Figure 3. (a) and (c) Recovery of the corrected histogram (black) from the total (red) after subtraction of background (cyan) from solutions (a) [2:1-dsDNA] ) 5 pM or (c) [2:1-dsDNA] ) 5 pM and [Alexa 488] ) [Alexa 647] ) 45 pM. (b) and (d) Fitting of corrected histogram (black) of the natural log of ratio of intensities from (a) and (c). The fitting parameters were f, the populations of the Gaussians at ratios f/f and 2 × f/f, and K2:1 related to the width of the second peak. K1:1 and f were fixed at known values. The total fitting function (blue) and the single populations centered at ratios f/f (light green) and 2 × f /f (dark green) are also shown. The recovered populations were as follows: (b) 63 ( 3% of a Gaussian centered at 1.72 and 37 ( 3% of a Gaussian centered at 0.86; (d) 62 ( 7% of a Gaussian centered at 1.91, and 38 ( 7% of a Gaussian centered at 0.96.
the same percentage of the population with a ratio close to 1 and 2 as for the pure 2:1-dsDNA, within experimental error (65 ( 9% for the population with a ratio close to 2) between 0.9 and 5 pM. Below 0.9 pM, the percentage of the population close to 2 decreased, possibly due to increased dissociation at these low concentrations. These experiments demonstrate that it is possible to recover the true ratio histogram for the 2:1 duplex dsDNA sample even in the presence of a high statistical background. In addition, the stoichiometry of the complexes can be also qualitatively judged through the analysis of the intensity histograms surface plots, a surface plot showing the event density for each IR,IB pair. The 2:1-dsDNA shows a higher density of events at large IR values, whereas for a 1:1-dsDNA, the surface plot is mainly symmetric (Figure S-2). We also calibrated the signal from 2:1-dsDNA samples in the presence of free dyes, having obtained a linear response of the significant coincidence percentage versus percentage of 2:1-dsDNA sample (Figure S-3). Once again, this calibration shows that the signal is sensitive only to the percentage of dual-labeled molecules, but not to the total concentration. Extraction of Kinetic and Thermodynamic Information. In order to explore the ability of the TCCD technique to determine low dissociation constants, as well as some kinetic information, the following model system was studied: a 9-bp double-stranded DNA, one strand labeled at the 5′-end with Alexa 488 and the
complementary strand labeled at the 5′-end with Alexa 647 (see Table 1). The theoretical melting temperature of this duplex DNA is 27 °C (using salt-adjusted melting temperature calculations).34 We found that at the low concentrations used for single-molecule experiments the majority of the strands are dissociated and only a small fraction of DNA is actually duplex. We used the method of analysis described above to determine the dissociation constant and follow the kinetics of the duplex dissociation. In these experiments, we increased slightly the 488-nm excitation laser power in order to compensate for FRET between the two fluorophores, and the measurements were performed at 8 °C so that the dissociation rate was sufficiently slow that it could be followed. We used two different buffers as described in Materials and Methods. The TNM2 buffer further stabilizes the duplex as the salt concentration is raised. The kinetic measurements were performed by diluting chilled stock solution of 9-bp duplex (10 nM) down to the single-molecule level (50-150 pM) and starting the measurement just after mixing. The coincidence events, and thus the coincidence levels, showed a clear decay with time (an example is shown in Figure 4). Dissociation rate constants (koff) were recovered by fitting the decay in coincidence levels with time to a single-exponential decay, and they are shown in Table 2. (34) http://www.basic.northwestern.edu/biotools/oligocalc.html.
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Figure 4. TCCD kinetics of dissociation of 9-bp dual-labeled duplex DNA at 75 pM, in the presence of 10 mM Mg2+ and 100 mM Na+ at 8 °C. The line shows a single-exponential fit, giving a decay time of 517 ( 26 s, i.e., a dissociation rate constant koff of (1.9 ( 0.1) × 10-3 s-1. Table 2. Recovered Dissociation Rate and Equilibrium Constants of the 9-bp Duplex at 8 °C and Two Different Salt Concentrations buffer
duplex concn (pM)
Kd (nM)a
koff (10-3 s-1)a
kon (106 M-1 s-1)b
TNM1 TNM1 TNM1 TNM1 TNM2 TNM2 TNM2
50 75 100 150 50 75 100
1.5 ( 0.4 2.2 (1.2 2.1 ( 0.6 2.6 ( 0.3 1.1 ( 0.3 1.2 ( 0.2 1.3 ( 0.1
1.2 ( 0.2 2.2 ( 0.3
0.8 ( 0.3 1.0 ( 0.6
1.6 ( 0.1 1.9 ( 0.2 2.5 ( 0.3
1.5 ( 0.5 1.6 ( 0.3 1.9 ( 0.3
a Errors represent standard deviation of three measurements. b Rate constant calculated as koff/Kd, and associated errors calculated through error propagation.
TCCD was then used to calculate dissociation equilibrium constants (Kd). We performed experiments in equilibrium waiting 45 min to allow dsDNA to reach equilibrium. For each measurement, the significant events burst rate was determined and the actual duplex concentration obtained by interpolation in the calibration rS versus [dsDNA] (Figure 2b). The actual dsDNA concentration is thus calculated through [dsDNA] ) f dsDNA ‚ r S, S ) 7.937 pM s (inverse of slope from Figure 2b). We with f dsDNA S calibrated the burst count rates of the 5′-end-labeled single strands and used this calibration to determine accurate concentrations of the dissociated single-stranded-DNA in the equilibrium measurements ([ssDNA]B ) f ssDNA rB and [ssDNA]R ) f ssDNA rR, where B R ssDNA ssDNA fB and f R are the single-channel detection efficiencies, with values of 1.331 and 1.367 pM, respectively). Since the concentrations of dsDNA and ssDNA are known, the equilibrium dissociation constant can then be determined through eq 7:
Kd )
[ssDNA]B[ssDNA]R [dsDNA]
)
rB)(f ssDNA rR) (f ssDNA B R f dsDNA rS S
(7)
The recovered Kd values are shown in Table 2. It is worth noting that consistently lower Kd values were obtained for TNM2 7714
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buffer, as expected for a more stable duplex DNA. The different Kd values recovered at different DNA concentrations for TNM2 buffer are statistically equivalent, as checked by means of Student’s t-tests. For TNM1 buffer, the average values 1.5 ( 0.4 and 2.6 ( 0.3 nM are different with a 95% of confidence level, whereas both of them are statistically equivalent to the other two values shown in Table 2. Therefore, the Kd values obtained at different DNA concentrations did not show significant differences within experimental error. Finally, the association rate constants (kon) can be obtained as Kd ) koff/kon. The recovered kon are in good agreement with those reported in the literature. The association rate constants of complementary strand hybridization depend on the length of the oligonucleotide, ionic strength, and base composition. For short oligonucleotides (six to eight bases), kon values between 106 and 107 M-1 s-1 have been reported.35,36 We should note that the 9-bp dual-labeled duplex shows strong FRET from Alexa 488 to Alexa 647. This would allow the kinetics to be followed by usual singlemolecule FRET measurements and would not require a two-color excitation setup. Indeed, we carried out measurements using 488nm excitation only and obtained similar dissociation rate constants (data not shown). The method was further validated by performing FRET bulk experiments to determine the equilibrium dissociation constant. We performed steady-state fluorescence measurements of the 9-bp duplex in a concentration range between 3 and 50 nM in TNM1 buffer and at 8 °C. At the highest concentrations, the duplex is mainly associated, whereas at lower concentrations, different dissociated fractions were detected. Measurements of the FRET efficiency in the duplex and fluorescence intensity of the single strands alone allow the estimation of the dissociation constant. The average value was 1.7 ( 0.9 nM, which is in good agreement with those recovered by the single-molecule TCCD technique. Further details of the FRET bulk measurements can be found in Supporting Information. DISCUSSION Here, we have improved the method of data analysis for the two-color, single-molecule coincidence fluorescence spectroscopy to detect low levels of coincident events due to molecular complexes in addition to chance coincident events due to monomers or fluorescent contaminants. We have shown that the subtraction of this statistical background is essential for accurate quantification of the relative number of complexes and their stoichiometry in cases of low levels of real coincidence events and high statistical backgrounds. This was done by developing two complementary methods to determine the statistical background in the same single experiment. Moreover, we have found that the two methods are generally in very good agreement with one another (for perfectly homogeneous data they are completely equivalent). These two methods may be defined as follows: (1) the mean coincidence rate of the two desynchronized combinations of adjacent file-pairs, averaged over the entire set of data (desynchronization approach) and (2) the expected chance coincidence rate due to the burst rates in synchronized file pairs, averaged over the entire set of data (frame-by-frame theoretical (35) Po ¨rschke, D. Biopolymers 1971, 10, 1989-2013. (36) Howorka, S.; Movileanu, L.; Braha, O.; Bayley, H. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 12996-13001.
estimation). The two methods are equivalent in the case of timehomogeneous burst rates. A third estimator may also be defined more simply as the expected chance coincidence rate due to the total average burst rates (method 3, overall theoretical estimation). If there is a large difference between either the first or second estimator and this third one, then this indicates that something may be wrong with a particular section of the data. For example, on rare occasions, a dust particle may cross the laser excitation volume, giving rise to a high signal from scattered light. In such cases, the anomalously large numbers of chance coincident events resulting from the dust particle are detected by methods 1 and 2 whereas method 3 is not able to detect that. In practice, this allows the problematic section of the data to be easily identified and excluded. Overall, this technique therefore also presents a reliable way to detect problems occurring during the measurements. Although only using the simplest theoretical approach (method 3) is rapid and does not require much data handling, we strongly recommend the estimation of chance coincidence using all three calculations and the careful comparison of the results. For experiments to determine the stoichiometry of the complex, the desynchronization approach is the only one able to recover the histograms from chance coincidence; the actual coincident events from the desynchronized frames can be used to construct the expected histograms of the chance events (the distribution of the function Z defined earlier). As we have shown, this can subsequently be subtracted from the total histogram in order to obtain the histogram from the significant coincident events. This has been demonstrated for a 2:1 duplex dsDNA in an excess of free dye. Furthermore, the methods developed here are useful not only for TCCD measurements of freely diffusing molecules but also in two-color excitation measurements performed in flow channels. We have also shown we can obtain linear calibrations of the corrected TCCD coincidence signal versus relative proportions of dual-labeled molecules, in the presence of large excesses of
single-labeled ones down to a level of 0.5% dual-labeled complex. Importantly, the parameter of interest, the significant coincidence level or corrected percentage of coincidence, only depends on the relative population of dual-labeled molecules and not on the level of the background. It can be very difficult to get accurate concentrations of complexes for single-molecule studies, so it is also important that the measurement we are making determines the relative population of complexes and does not rely on determining absolute concentrations. Based on our detection limit, we can study equilibria with dissociation constants as large as 3 nM (see Figure S-4). This will be of particular use in cases where the dissociation constant of the complex to be studied is nanomolar or where it is not possible to prepare a high fraction of the complex as is the case in many complicated biochemical preparations. All these refinements together extend the possible applications of single-molecule methods allowing more sensitive studies of complex biomolecular systems. ACKNOWLEDGMENT A.O. thanks Consejeria de Innovacion, Ciencia y Empresa (Junta de Andalucia) for a postdoctoral fellowship and R.W.C. the Biotechnology and Biological Research Council, UK, for his studentship. We gratefully acknowledge the contribution of Dr. Liming Ying for constructive criticism and suggestion during the development of these methods. SUPPORTING INFORMATION AVAILABLE Additional information and figures as noted in the text. This material is available free of charge via the Internet at http:// pubs.acs.org. Received for review June 21, 2006. Accepted September 15, 2006. AC061122Y
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