Correlation-Matrix Analysis of Two-Color Coincidence Events in

Article pubs.acs.org/ac

Correlation-Matrix Analysis of Two-Color Coincidence Events in Single-Molecule Fluorescence Experiments Idir Yahiatène,† Sören Doose,‡ Thomas Huser,†,§ and Markus Sauer*,‡ †

Applied Laser Physics and Laser Spectroscopy, Bielefeld University, Universitätsstrasse 25, 33615 Bielefeld, Germany Biotechnology and Biophysics, Julius-Maximilians-University Würzburg, Am Hubland, 97074 Würzburg, Germany § Center for Biophotonics Science & Technology, University of California, Davis, Sacramento, California 95817, United States ‡

S Supporting Information *

ABSTRACT: We introduce a robust and relatively easy-to-use method to evaluate the quality of two-color (or more) fluorescence coincidence measurements based on close investigation of the coincidence correlation-matrix. This matrix contains temporal correlations between the number of detected bursts in individual channels and their coincidences. We show that the Euclidian norm of a vector Γ derived from elements of the correlation matrix takes a value between 0 and 2 depending on the relative coincidence frequency. We characterized the Γ-norm and its dependence on various experimental conditions by computer simulations and fluorescence microscopy experiments. Single-molecule experiments with two differently colored dye molecules diffusing freely in aqueous solution, a sample that generates purely random coincidence events, return a Γ-norm less than one, depending on the concentration of the fluorescent dyes. As perfect coincidence sample we monitored broad autofluorescence of 2.8 μm beads and determined the Γ-norm to be maximal and close to two. As in realistic diagnostic applications, we show that two-color coincidence detection of single-stranded DNA molecules, using differently labeled Molecular Beacons hybridizing to the same target, reveal a value between one and two representing a mixture of an optimal coincidence sample and a sample generating random coincidences. The Γ-norm introduced for data analysis provides a quantifiable measure for quickly judging the outcome of single-molecule coincidence experiments and estimating the quality of detected coincidences.

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provide a more accurate characterization of molecular interactions.4−13 Combined with single-molecule fluorescence spectroscopy FRET has been used successfully to study interactions of donor/acceptor labeled proteins as they diffuse through the detection volume of a confocal fluorescence microscope.5−13 FRET, however, requires that the fluorophores are in close proximity which is not always possible when labeling proteins and necessitates detailed knowledge of specific binding and interaction sites of the macromolecules involved. Alternatively, two spectrally different fluorophores can be excited simultaneously and two-color coincidence detection on two spectrally separated detectors can be used to determine joint diffusion (colocalization) and, thus, binding of the two interaction partners. Similarly, multicolor fluorescence crosscorrelation spectroscopy can be applied to study molecular interactions in the nanomolar concentration range.14,15 Furthermore, single-molecule multicolor coincidence detection was used for the detection of target molecules down to the pico- to femtomolar concentration range and thus volunteers as

he sensing and diagnostic analysis of pathogens or disease markers in its currently most widely adopted form requires the highly specific and sensitive detection of proteins, DNA, or RNA. This necessitates the development of methods that can identify the complex interplay of multiple macromolecules, such as antigen−antibody interactions or DNA hybridization. For instance, the popular enzyme-linked immunosorbent assay (ELISA) involves a surface-immobilized antibody that captures the target molecule and pulls it onto a surface. Then, another primary antibody is required for the identification of the target, sometimes even requiring a secondary antibody to accomplish the labeling step. To perform such assays in their most sensitive form, optical methods that can probe and analyze single fluorescent molecules are essential. Such single-molecule fluorescence spectroscopy experiments typically make use of multiple, spectrally distinguishable fluorophores to analyze molecular interactions between complex molecular systems.1−3 Fluorescence resonance energy transfer (FRET) experiments, where the excitation energy of a donor fluorophore is transferred radiationless to another, red-shifted acceptor fluorophore over 2−10 nm distances can be used to determine donor/acceptor distances and distance changes and thus © 2012 American Chemical Society

Received: November 15, 2011 Accepted: February 16, 2012 Published: February 16, 2012 2729

dx.doi.org/10.1021/ac2030283 | Anal. Chem. 2012, 84, 2729−2736

Analytical Chemistry

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the binding sequence of the penecillin binding protein on Streptococcus pneumoniae DNA:22 gaccttattcaaagtctcaacggctgtgacatttcgtgattgttgaagag catattgcagagtaatattaccgaaatatgctctatcccagttgtagaca. The areas where the cDNA hairpin molecules can hybridize with the target are plotted italic and bold. The first hairpin is 5′-modified with ATTO565 and 3′-modified with Black Hole Quencher 2 (BHQ2, IBA). The sequence is CCCTGcaatatgctcttcaaCAGGG where the nucleotides shown in capital letters form the stem. The second hairpin is 5′modified with ATTO647N and 3′-modified with Black Berry Quencher 650 (BBQ650, IBA) and has the following sequence: GGGTCTacaactgggatagAGACC. The two hairpin samples were mixed at 10−10 M concentrations with three different concentrations of the single-stranded target DNA in PBS containing 0.02% Tween20. The mixture was heated to 95 °C for 5 min and subsequently cooled at a rate of 1 °C per minute to room temperature in a thermocycler (PTC-100 Programmable Thermal Controller, MJ Research Inc.) to ensure efficient hybridization. Confocal Setup for Two-Color Coincidence Detection. A diode laser (Cube 25 mW; Coherent, Dieburg, Germany) operating at 638 nm and a solid state laser emitting at a wavelength of 532 nm (Compass 215M-10; Coherent, Dieburg, Germany) were collimated and simultaneously coupled into an oil immersion microscope objective (60x, 1.35 NA; Olympus, Hamburg, Germany) using a dichroic beam splitter (540 DCXR; Chroma, Bellows Falls, VT, USA). The fluorescence emitted by the sample molecules was collected by the same objective lens, spatially filtered by a 100 μm pinhole and spectrally separated by a 640 nm dichroic mirror (640 DCXR; Chroma, Bellows Falls, VT, USA). Further filtering for spectral separation was accomplished by a combination of bandpass and long-pass filters (“green” channel: 582/50 bandpass, RazorEdge 568 long-pass and HQ 600/40 M bandpass; “red” channel: 692/40 bandpass, RazorEdge 647 long-pass and Brightline 670/30; all from Semrock, NY, USA). The fluorescence signals were detected by two avalanche photodiodes (APD) working in the photon counting mode (SPCM-AQR-15; Perkin-Elmer, Waltham, Massachusetts, USA). We used laser excitation with intensities of 550 μW and 900 μW at 638 and 532 nm, respectively, focused to a diffraction-limited spot in solution. Single photons detected by the two APDs were registered with a digital counting board (PCI-6602, National Instruments, Ennetbaden, Switzerland) providing a time resolution of 12.5 ns and analyzed by a homemade software written in LabView (National Instruments). Microfluidic Channel. The microfluidic flow channel used in the experiments was made from a poly(methyl methacrylate) (PMMA) substrate at the dimensions of a conventional microscope glass slide (76.15 mm × 26 mm × 3.9 mm). Using a computer-controlled milling machine with a fine tip with 300 μm diameter, a ∼4.8 cm long linear channel with a depth of 100 μm was milled into the plastic material. The PMMA substrate defines the bottom of the flow channel which is in contact with the immersion oil. To cover the channel, we used commercially available optically clear, one-sided sticky tape (TesaFilm, Crystal clear, Tesa, Hamburg, Germany) with a thickness of 40 μm. The channel is then furnished with two 3 mm diameter holes at either end to permit the connection with flexible tubing. Through one of the holes commercially available flexible HPLC tubing connects the channel with a motorized syringe pump (PHD2000; Infusion Harvard

an excellent method to sensitively probe molecular interactions.16−21 On the other hand, coincidence detection cannot distinguish between real and random coincidences. To quantify the number of interacting DNA or protein molecules in solution by two-color coincidence detection experiments a quantitative measure is needed that allows us to judge the specificity and sensitivity of the interacting partners. Here, we introduce an analysis method based on constructing a correlation-matrix and a related feature vector with an Euclidian norm that provides a parameter for characterization of multicolor coincidence detection experiments. The analysis provides a straightforward way to judge the quality of coincidence measurements with regard to the contribution from real and random coincidences. Applying the correlation matrix method to a two-color sample we demonstrate that one can clearly distinguish DNA samples with true coincidence events from samples with mere random coincidence events of freely diffusing dyes. We show that the probability of random coincidence events grows with increasing concentration of unbound dye molecules. The correlation matrix method returns a value for what we call the Γ-norm lΓ ∈ [0,2] for two-color coincidence detection experiments. The larger the deviation from the maximum lΓ value of two, the smaller is the ratio between real and random coincidence events that are present in the sample. The Γ-norm approaches values of one or below for mere random coincidence events of two freely diffusing dyes. These characteristics of the Γ-norm are investigated by computer simulations and in single-molecule experiments suggesting a concise and easily applicable analysis scheme.

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EXPERIMENTAL SECTION Dyes. The organic fluorescent dyes ATTO647N and ATTO565 (ATTO-TEC GmbH, Siegen, Germany) dissolved in phosphate buffered saline (PBS) buffer were used as freely diffusing fluorescent dyes. Samples that generate random coincidence events on two spectrally different channels were prepared mixing ATTO647N at 10−11 M with different concentrations of ATTO565 molecules ranging between 10−10 and 10−12 M. As optimal coincidence sample we used the intrinsic, spectrally broad autofluorescence signal of M280 magnetic microparticles (Invitrogen GmbH, Darmstadt, Germany) with a diameter of 2.8 μm. The beads were excited at 532 and 638 nm simultaneously and detected on both channels with comparable fluorescence intensities. To generate an optimal coincidence sample, we diluted 1 μL of the M280 beads (∼6 × 103 particles/μL) in 100 μL PBS and used a micrometer-sized channel to control bead movement through the laser focus at different flow rates (0−40 mL/h). The M280beads’ lateral movement in solution due to diffusion or gravitational effects are negligible at increased flow rates. DNA. For optimal coincidence detection we further used a 20mer double-stranded DNA that is labeled with ATTO565 at the 5′-terminal of the poly-T strand and ATTO647N at the 5′terminal of the complementary poly-A strand. The sample was commercially synthesized and labeled (IBA, Gö ttingen, Germany). Our realistic two-color coincidence detection sample consists of a model DNA sequence chosen from the bacteria Streptococcus pneumoniae causing lower respiratory tract infections that is targeted by two cDNA fragments designed as hairpin structure. All DNA samples were commercially synthesized (IBA, Berlin, Germany). The synthetic target sequence with a length of 100 nucleotides was adopted from 2730



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This Γ-norm will take values between zero and two with the maximum value resulting from an ideal two-color coincidence sample. Data Simulation. For numerical characterization of the Γnorm, we simulated single-molecule time traces for two channels. For randomized data generation, we assume that in each time bin the detected number of photons s(t) is Poissondistributed (eq 3) with

Apparatus, Holliston, Massachusetts, USA). The other hole serves as outlet for the solvent. Data Processing. Data processing is based on previously described standard methods for identifying and analyzing single-molecule events, so-called photon bursts.23 We analyzed the multichannel intensity time traces obtained by multicolor fluorescence detection experiments by first binning photon arrival times into 1 ms bins. In a typical experiment we measured signal peaks with kHz count rates in the most intense bins. Binning on the millisecond time scale is reasonable since the characteristic transition times of all observed macromolecules through the diffraction-limited laser spot is of that order. We then identified photon bursts independently in each channel as those bins with intensities above a certain threshold value. A commonly used threshold definition is the mean signal intensity μ plus a certain multiple of the standard deviation σ as calculated from the complete time trace.24 Here, we use μ + 4σ determined from a low concentrated sample as the threshold criterion to ensure that single fluorescent molecules are clearly discriminated from background fluorescence. For the present work we implemented an algorithm written in C++ (Dev C++ Version 4.9.9.2, Bloodshed Software) to identify molecular events and perform all further analysis. After photon burst identification, we separate the recorded time traces into N sections and calculate the number of bursts Bi(r) in each channel (i = 1,2 representing e.g. green and red emitting fluorophores) and for each section (r = 1, ..., N). In addition we calculate for each section the sum of all detected bursts over all channels Bs(r), and the number of coincidence events in all channels Bc(r). With these four parameters we construct the corresponding 4 × 4 correlation-matrix defined as ⎡1 ⎢ ⎢ χ1,2 X=⎢ ⎢ χ1, s ⎢ ⎢χ ⎣ 1, c

Pλ(s) =

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RESULTS AND DISCUSSION Simulation of Coincidence Events Characterized by Correlation Analysis. In a first step we characterized the described analysis routine by performing computer simulations. From randomly generated signal traces we calculated the Γnorm under different conditions like burst concentrations, number of sections, and sample mixtures. After generating single-burst data on two channels using a random generator from the Mathematica software package, we identified those bins of the total 105 independent bins that carry a photon burst. Since no background signal was included, the threshold set to one discriminated between burst and no burst, discarding any information on the burst signal intensity. Generation of two independent burst streams representing two different channels allows counting of the number of bursts in each channel and the occurring coincidences in both channels. We assume that for a given concentration of fluorophores the burst size in each bin is Poisson distributed with a mean and variance of λ (eq 3). The number of bursts, as well as their average signal, rises with increasing λ indicating that λ represents a concentration of detected single molecules in a comparable experiment. In Figure 1 the number of detected bursts relative to the total number of bins in a single channel is shown. This number is equal to the probability of burst occurrence in each bin. In addition, the relative number of coincidence events in both simulated channels is determined and the ratio between coincidence and burst events displayed. Calculation of the Γnorm as function of λ (representing fluorophore concentration) shows that the Γ-norm increases with increasing dye concentration due to the increasing number of random coincidence events (Figure 1B). However, for any concentration range in which single-molecule bursts can be detected in a confocal microscope the Γ-norm stays below one. As technical peculiarity it is important to note that the calculated Γ-norm depends on the number of sections in which the total signal trace is divided for calculation of the correlation matrix (Figure S1 in the Supporting Information). It appears and indeed is reflected in the experiments shown further down, that the Γ-norm estimate decreases with increasing number of

χ2,1 χs ,1 χc ,1 ⎤ ⎥ 1 χs ,2 χc ,2 ⎥ ⎥ χ2, s 1 χc , s ⎥ ⎥ χ2, c χs , c 1 ⎥⎦

χi , j = 1 ∑N (B (r ) − Bi )×(Bj (r ) − Bj ) N r=1 i 1 1 ∑N (B (r ) − Bi )2 × ∑N (B (r ) − Bj )2 N r=1 i N r=1 j (1)

where Bi and Bj denote the corresponding mean values over all N sections. Normalization and the symmetry of correlation coefficients causes the correlation matrix to be a Hermitian matrix with all main diagonal elements being equal to one. We chose only few of the correlation coefficients, namely χ1,2, χ1,c, χ2,c, and χs,c, for further analysis and disregarded χs,1 and χs,2. In a final step we arrange these correlation coefficients as components of a feature vector Γ = (χ1,2, χ1,c, χ2,c and χs,c) and calculate its Euclidian norm (eq 2) χ1,2 2 + χ1, c 2 + χ2, c 2 + χs , c 2

(3)

The parameter λ scales with and thus represents the concentration of molecules and is kept between 10−3 and 3. Random data was generated using Mathematica 8 (Wolfram Research, Champaign IL, USA) for up to 105 data points (representing time bins) and further analyzed as described above. We tested the behavior of the Γ-norm for different concentrations of emitters in two independent channels, two perfectly coinciding channels, and various mixtures of both. Background was always neglected since sufficiently large threshold values for photon burst identification eliminate background influence.

where each χi,j = corr(Bi,Bj) is a correlation coefficient calculated from the counted burst numbers with indices i,j ∈ {1,2,c,s}. The normalized correlation coefficients are calculated by eq 1

lΓ =

λs −λ e s!

(2) 2731



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Figure 1. Simulated single-molecule data on two independent detection channels. (a) Single burst events are simulated in 105 bins at various λ (representing concentrations) (filled squares) and random coincidences are determined (open circles). Inset: Ratio between number of coincidences and number of single channel bursts is given for each λ. (b) Γ-norm is calculated for each λ as mean from 100 random data sets and the standard deviation is displayed as error bar. The numbers of bursts or coincidence events are all normalized to the total number of bins analyzed. The y-labels thus represent a probability for each bin to carry a burst or coincidence event.

Figure 2. Simulated single-molecule data of various mixtures of perfect coincidence events and independent burst events on two channels. (a) Single burst events are simulated in 105 bins at a constant concentration of coincidence events (λ = 0.2) and various concentrations (i.e., various λ) of independent bursts events (filled squares). Total number of detected coincidences are determined (open circles). Inset: Ratio between number of coincidences and number of single channel bursts is given for each λ. (b) Γ-norm is calculated for each λ as mean from 100 random data sets and the standard deviation is displayed as error bar. The numbers of bursts or coincidence events are all normalized to the total number of bins analyzed. The y-labels thus represent a probability for each bin to carry a burst or coincidence event.

sections but approaches a limiting value at about 100 sections. We therefore used 100 sections for all further analysis unless indicated otherwise. In Figure 2 the behavior of the Γ-norm is shown for a mixture of pure and random coincidence samples. When mixing a perfect coincidence sample (here simulated as identical bursts events on two channels Poisson distributed with λ = 0.2) with independent burst events (simulated on both channels with various λ as displayed) the Γ-norm decreases from its maximum value two toward one. At the highest λ for the contribution from independent bursts the Γ-norm increases slightly because of the increasingly larger number of random coincidences. The same behavior is observed when a mixture of equal concentrations (equal λ) of pure coincidence and independent burst events is simulated (Figure S2 in Supporting Information). From these simulations it appears that the Γnorm does not directly reflect the ratio of pure coincidence and independent burst events, but rather the ratio of detected coincidences and total number of bursts (at least as long as the two detection channels display the same total number of bursts). In Figure S2 in Supporting Information, the Γ-norm increases because at larger λ more random coincidences contribute similar to the behavior displayed in Figure 1. However, it is important to note, that for reasonable singlemolecule concentrations, the Γ-norm varies between 1.0 and 1.4, a value that is clearly above the Γ-norm of a purely random coincidence sample (as shown in Figure 1).

Experimental Detection of Random Coincidences. Motivated by the use of the described correlation matrix, and the Γ-norm in particular, for characterizing a single-molecule measurement in terms of coinciding signal contributions, we measured the number of coincidence events that are recorded from two noninteracting molecules (ATTO565 and ATTO647N) mixed in solution at various concentrations. Figure 3A shows measured rates for detected bursts on either channel and coincident bursts on both channels as observed in a typical fluorescence single-molecule experiment with different dye ratios. The calculated rates are shown as function of ATTO565 concentration (10−11−10−12 M) at constant ATTO647N concentration (10−11 M). As expected the coincidence rate increases with increasing concentration of ATTO565 and is on the order of 10% of the total detected burst rate (a ratio similar to the values found in the corresponding computer simulations). A linear fit indicates that dye concentration and detected burst rates are directly proportional to each other, as expected. At a concentration of 10−12 M for ATTO565 we found coincidence events corresponding to a coincidence rate of 0.43 ± 0.22 Hz (standard deviation of the total measurement sectioned into three parts). At equal concentrations of 10−11 M for both dyes we found coincidence events corresponding to a coincidence rate of 4.1 ± 0.3 Hz. The total acquisition time was 540 s in all 2732



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found coincidence rates between 0.5 and 5 Hz (Figure 4A). From burst and coincidence identification we determined the

Figure 3. Single-molecule data measured on two separate detection channels for ATTO647N and ATTO565 freely diffusing at different ratios, where the concentration of ATTO647N is fixed at 10−11 M. The sample was excited simultaneously at 532 nm with a power of 900 μW and at 638 nm with 550 μW. (a) The mean burst rates are displayed as detected on the red channel (filled squares) and on the green channel (empty circles) together with the random coincidence rate (filled triangles). The lines are linear fits as guide for the eye and arrows point at corresponding axes. The standard deviation determined from 3 measurements defines the error bars. (b) The Γnorm is calculated as function of the number of sections for different ATTO565 concentrations ranging from 10−12 to 10−11 M.

Figure 4. Single-molecule data measured on two separate detection channels for 2.8 μm M280 micro particles flown through a microfluidic device with a concentration of ∼10−14 M. The samples were excited simultaneously at 638 and 532 nm with excitation powers of ∼630 μW.(a) The coincidence rate was measured as a function of flow velocity (or volume current) to artificially raise the apparent concentration. Error bars represent the standard deviation estimated from three measurements. (b) The Γ-norm is calculated as a function of the number of sections for different flow rates ranging from 0 to 40 mL/h.

measurements. For calculation of the Γ-norm, we divided the total time trace into 10−100 sections. As seen in simulated data, the Γ-norm decreases slightly with increasing numbers of sections (Figure 3B) but approaches a limiting value below one. As each value for the Γ-norm is calculated from a single data set (and not from 100 data sets as presented for the simulated data) the error appears larger and shields the concentration dependence to a certain degree. However, it is clear that the Γnorm remains below one for all concentrations and decreases with decreasing concentration. Experimental Detection of Pure Coincidences. Next, we performed similar experiments with 2.8 μm M280 beads kept at a constant dilution of one in hundred in PBS buffer, corresponding to a concentration of ∼10−14 M. The beads exhibit only slow diffusion and tend to sediment due to their relatively large size. In order to increase the detection rate beads were flown through a 300 μm microfluidic channel. Simultaneous excitation at 532 and 638 nm generates an autofluorescence signal that is high enough for detection in the two spectrally separated detection channels. The fluorescence trajectories measured under different applied flow rates demonstrate that autofluorescent beads can be used as “perfect” coincidence sample for instrument calibration. Varying the flow rate through the microfluidic channel from 0 to 40 mL/h we

fraction of coincidence events relative to the total number of detected bursts to be larger than 85%. The Γ-norm (Figure 4B) again decreases for the number of sections smaller than 100, but approaches values around 1.9 without any dependence on flow rate (or correspondingly total burst rate). The bead sample thus represents a nearly pure coincidence sample yielding maximal Γ-norm values. In a second experiment, we studied double-labeled DNA with ATTO565 and ATTO647N attached to double-stranded DNA and separated by 20 base pairs. As shown in Figure 5, the sample does not result in a perfect coincidence sample. Both, total burst and coincidence rates as well as the Γ-norm reflect that the sample consists of a mixture of a real coincidence sample and single fluorescent emitters arising most probably due to insufficient hybridization. Double-labeled DNA exhibiting only single emitters can further result from inactive or photobleached fluorophores. The fact that burst and coincidence rate approach each other at concentrations around 10−10 M most likely reflects the increasing amount of overlapping single-molecule events (Figure 5A). The Γ-norm, 2733



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Experimental Detection of Coincidence Events As Diagnostic Tool. To assess the coincidence data obtained from a sample with diagnostic relevance, we used singlestranded DNA molecules with a length of 100 bases as target for two differently labeled (ATTO647N and ATTO565) Molecular Beacons (MBs).25−27 MBs are fluorescently labeled oligonucleotides that form a loop-stem structure. In the closed state the terminally conjugated fluorescent dye is quenched efficiently by a quencher attached to the other end of the stem. We used the so-called Black Hole Quencher 2 (BHQ2) for ATTO565 and the Black Berry Quencher (BBQ650) for ATTO647N quenching, respectively. Upon hybridization between the MB’s loop sequence and the complementary target DNA sequence the stem-loop structure is opened up and fluorescence recovers. The two MBs used in our experiments show a 20−30 fold increase in fluorescence intensity upon addition of a 10-fold excess of target sequence (Figure S3 in Supporting Information). Hybridization of both MBs to the same DNA sequence results in the detection of a coincidence event demonstrating the presence of the target DNA with high sensitivity and high specificity. The advantage of using quenched MBs for coincidence detection of DNA sequences lies in the fact that unbound MBs do not contribute to the generation of random, probe-unrelated coincidence events.28−30 Furthermore, the use of efficiently quenched probe molecules enables the use of higher probe concentrations shifting the equilibrium to the hybridized state and increasing the achievable detection sensitivity. As seen in Figure 6A, the coincidence rate observed for a mixture of MB probes at constant 10−10 M concentration and target DNA at concentrations between 0 and 10−10 M is between 0.03 and 2 Hz. For comparison, we observed a random coincidence rate of ∼4 Hz using equimolar dye concentrations of 10−11 M for ATTO647N and ATTO565 (Figure 3A), a value that is hundredfold larger than that observed for pure MB mixtures without any target DNA added. This comparison highlights the advantage of quenched hairpin probes for DNA coincidence detection: because nonhybridized MB probes are efficiently quenched the chance for random coincidence events is substantially decreased. For target DNA detection by twocolor coincidence with quenched DNA hairpins we determine the Γ-norm to be around 1.4 independent of the target concentration (Figure 6B), whereas the Γ-norm decreases to less than 0.5 in the absence of the target DNA sequence. Even at a target DNA concentration of 10−13 M a significantly elevation of the Γ-norm above random coincidence level for the quenched MB sample is observed indicating the high sensitivity of this parameter. The measured Γ-norm of ∼1.4 at higher target concentrations is lower than the value expected for an ideal coincidence sample yet definitely higher than the value of 0 to 1 measured for random coincidence events (Figure 3B). The deviation from the Γ-norm for a pure coincidence value is mostly due to the fact that some target DNA strands also hybridized to only one of the two MBs and thus contribute to random coincidence events.

Figure 5. Single-molecule data measured on two separate detection channels for 20 bp poly-(AT) DNA duplexes doubly labeled with ATTO647N and ATTO565. The samples were excited simultaneously at 638 and 532 nm with excitation powers of 600 μW and 900 μW. (a) The coincidence rate (green triangles), and the burst rates of the red (black squares) and green (red circles) channel were recorded as a function of DNA concentration. The error bars denote the standard deviation resulting from 4 measurements. (b) The Γ-norm is calculated as a function of the number of sections for various DNA concentrations ranging from 10−12 to 10−10 M.

however, yields a consistent value of about 1.5 for all concentrations above 10−11 M. This value is well above the Γ-norm that can be reached with a random coincidence sample (i.e., two different freely diffusing dyes) but still smaller than the Γ-norm of a pure coincidence sample. At concentrations below 10−11 M, the Γ-norm drops below one indicating an increasing contribution from single emitters. This behavior indicates that the double-fluorophore sample contributes less to the total number of detected bursts. In a control experiment we identified background fluorescence on the green channel that originates from the addition of the detergent Tween20. In addition, the brightness of the green fluorophore in the DNA samples is reduced since the donor/acceptor distance in the DNA sample of ∼6.8 nm (corresponding to a 20 bp separation) enables Förster resonance energy transfer. With decreasing concentrations of double-labeled DNA sample, random coincidences between the single-label bursts of detergent background and the FRET-amplified red signal of doublelabeled DNA samples or unhybridized red-labeled DNA strands contribute increasingly to the gamma-norm estimate. This observation nicely demonstrates that the gamma-norm serves as quality parameter indicating which molecular species contribute most to the observed coincidences.

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CONCLUSIONS In conclusion, we have demonstrated how the correlation matrix provides a quantitative measure for the quality of twocolor coincidence detection experiments and the extent of molecular interactions. The reliability of the method, which can be easily expanded to three or more colors, was demonstrated by the experimental study of three different samples. Analyzing 2734



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quality of single-molecule multicolor coincidence experiments that is widely applicable in single-molecule diagnostic applications.

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ASSOCIATED CONTENT

S Supporting Information *

Supporting material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +49 931 31-88687. Fax: +49 931 31-84507. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the EU-FP7 project TheraEDGE. REFERENCES

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Figure 6. Single-molecule data measured on two separate detection channels for a mixture of 100 bases synthetic single-stranded target DNA sequence and two quenched hairpin-shaped oligonucleotides hybridizing to different regions on the same target sequence. The samples were excited simultaneously at 638 and 532 nm with excitation powers of ∼550 μW and ∼900 μW. (a) The burst rates detected on the red (filled squares) and on the green channel (open circles) and the coincidence rate (black triangle) were recorded as a function of target DNA concentration. The arrows point at the corresponding axis. The error bars denote standard deviations resulting from 3 measurements. (b) The Γ-norm is calculated as a function of the number of sections for different target concentrations ranging from 0 to 10−10 M.

the experiments with autofluorescent beads measured at different flow rates we obtain a mean Γ-norm around 1.9 (Figure 4), a value close to two which is the theoretically expected Γ-norm for a perfect coincidence sample. Furthermore, our data demonstrate that the Γ-norm remains unaffected by the sample concentration (induced here by different flow velocities in the microfluidic channel) in case of a perfect coincidence sample. A change in the Γ-norm with increasing sample concentration provides a clear sign for the presence of random coincidence events. A mixture of two independent and spectrally different fluorescent dyes shows only random coincidence events reflected in a Γ-norm between zero and one (Figure 3). We observe an increase in the Γ-norm with increasing dye concentration in the experiments with the two noninteracting dyes ATTO647N and ATTO565 and determine a Γ-norm of around 1 for equimolar 10−11 M dye concentrations. A DNA sample, as used in realistic diagnostic detection assays, that consists of two quenched DNA hairpins specifically hybridizing to a single-stranded target DNA exhibits a Γ-norm well above one and in between the two extreme values measured for a perfect and purely random coincidence sample (Figure 6). Computer simulations confirmed the robustness of the Γ-norm and proved that by determining the Γ-norm we now have a quantifiable parameter to judge the 2735



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Correlation-Matrix Analysis of Two-Color Coincidence Events in

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