On the Origin of Broadening of Single-Molecule FRET Efficiency

Apr 16, 2010 - ... of Single-Molecule FRET Efficiency Distributions beyond Shot Noise Limits. Stanislav ... E-mail: stanislav.kalinin@uni-duesseldorf...
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J. Phys. Chem. B 2010, 114, 6197–6206

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On the Origin of Broadening of Single-Molecule FRET Efficiency Distributions beyond Shot Noise Limits Stanislav Kalinin,*,† Evangelos Sisamakis,†,‡ Steven W. Magennis,†,§ Suren Felekyan,† and Claus A. M. Seidel*,† Institut fu¨r Physikalische Chemie, Lehrstuhl fu¨r Molekulare Physikalische Chemie, Heinrich-Heine-UniVersita¨t, UniVersita¨tsstrasse 1, Geb 26.32, 40225 Du¨sseldorf, Germany, and Department of Applied Physics, Group of Experimental Biomolecular Physics, The Royal Institute of Technology, AlbanoVa UniVersity Center, SE-106 91 Stockholm, Sweden ReceiVed: January 2, 2010; ReVised Manuscript ReceiVed: March 10, 2010

Single-molecule FRET experiments on freely diffusing rigid molecules frequently show FRET efficiency (E) distributions broader than those defined by photon statistics. It is often unclear whether the observed extra broadening can be attributed to a physical donor-acceptor distance (RDA) distribution. Using double-stranded DNA (dsDNA) labeled with Alexa488 and Cy5 (or Alexa647) as a test system, we investigate various possible contributions to the E distribution width. On the basis of simultaneous analysis of donor and acceptor intensities and donor lifetimes, we conclude that dsDNA chain dynamics can be ruled out as a possible reason for the observed E distribution broadening. We applied a set of tools to demonstrate that complex acceptor dye photophysics can represent a major contribution to the E distribution width. Quantitative analysis of the correlation between FRET efficiency and donor fluorescence lifetime in 2D multiparameter histograms allows one to distinguish between broadening due to distinct FRET or dye species. Moreover, we derived a simple theory, which predicts that the apparent distance width due to acceptor fluorescence quantum yield variations increases linearly with physical donor-acceptor distance. This theory nicely explains the experimentally observed FRET broadening of a series of freely diffusing labeled dsDNA and dsRNA molecules. Accounting for multiple acceptor states allowed the fitting of experimental E distributions, assuming a single fixed donor-acceptor distance. 1. Introduction Single-molecule Fo¨rster resonance energy-transfer (FRET) measurements are widely used to study heterogeneities often found in biological systems.1-3 Recently, quantitative descriptions of FRET efficiency distributions4-8 have become available, such as probability distribution analysis (PDA)4,9,10 or proximity ratio histogram (PRH) analysis.7 PDA and PRH are potentially able to separate photon shot noise from distributions of donor-acceptor distances (RDA), which makes these methods very promising for studies of structural heterogeneities on the single-molecule level. Surprisingly, in several experiments on rather rigid molecules, such as double-stranded DNA (dsDNA), significant broadening of FRET efficiency (E) distributions beyond shot noise limits has been observed.4,7,11 In the case of dsDNA, broadening of E distributions has been reported by several independent groups4,7,11,12 and is, therefore, unlikely to be due to a simple instrumental artifact. On the other hand, it is generally accepted that DNA chain dynamics (and fluorophore linker dynamics) occur on a time scale of microseconds or faster (see, e.g., refs 13-16). From a structural viewpoint, extra FRET broadening is unexpected in this case because it should be averaged by the millisecond “integration time” of intensity-based single-molecule FRET measurements. Other relatively flexible molecules such * To whom correspondence should be addressed. E-mail: stanislav.kalinin@ uni-duesseldorf.de (S.K.); [email protected] (C.A.M.S.). † Heinrich-Heine-Universita¨t. ‡ The Royal Institute of Technology. § Present address: School of Chemistry and The Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.

as polyproline peptides and small unfolded proteins have also shown additional broadening of E distributions.17-20 The question thus arises, how much of the additional broadening of E distributions is due to structural heterogeneity or slow dynamics? Although in a few cases3 nearly shot noise limited E distributions have been observed, it is still generally unclear whether a fixed FRET rate (fixed RDA) always results in the theoretically predicted distribution width. In the case of dsDNA, the question of whether the extra broadening of FRET distributions should be attributed to slow chain dynamics of dsDNA is still open.4,7,11,12 In this work, evidence against such an interpretation of PDA results is presented. It is based on the analysis of burst lifetime distributions and a comparative study of DNA molecules with completely different structure. We demonstrate that for commonly used FRET pairs, variations of the acceptor fluorescence quantum yield provide the main (although not necessarily the only) contribution to the observed apparent FRET efficiency distribution broadening. If a Cy5 or an Alexa647 fluorophore is used as a FRET acceptor, heterogeneity of its fluorescence properties is not averaged out on the millisecond time scale. We will show that variations of the acceptor fluorescence quantum yield lead to a linear dependence of the apparent distance distribution width on its mean. For the case of dsDNA labeled with the Alexa488-Cy5 FRET pair, accounting for multiple acceptor populations explains the FRET efficiency distribution width, producing a satisfactory PDA fit without a need to assume a distribution of donor-acceptor distances.

10.1021/jp100025v  2010 American Chemical Society Published on Web 04/16/2010

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2. Theoretical Prerequisites 2.1. Basic Theory of PDA. The theory of PDA is described in details in refs 4, 9, and 10. Applying PDA to our FRET experiments, where the signal of the donor and acceptor is registered by green and red detectors, respectively, the distribution of green and red signal P(SG, SR) is calculated by eq 1

spectral crosstalk R and background signal B in the green (G) and red (R) detection channel (eq 2b). To convert the signal intensity ratio SG/SR (or fluorescence ratio FD/FA) into a distance using PDA, we consider eq 2b for the calculation of the fluorescence F and use eq 3

RDA ) R0r[ΦFAFD /FA]1/6 P(SG,SR) )

∑

FG+BG)SG;FR+BR)SR

P(F)P(FG,FR |F)P(BG)P(BR)

(1) In eq 1, F and B denote the number of fluorescence and background photons per time bin (time window) of a fixed length, S is the total measured signal (S ) F + B), and P(F) and P(B) represent the fluorescence and background intensity distributions, respectively. The subscripts refer to green (G) and red (R) detection channels, which cover the donor and acceptor emission peaks, respectively. The distribution P(F) can be deconvoluted from the experimental signal intensity distribution P(S) as described.9 The distribution P(SG, SR) is typically used to generate 1D histograms of FRET efficiency E or any other FRET-related parameter (e.g., proximity ratio SR/(SG + SR) or SG/SR ratio) and fitted to experimental data. For a single FRET state, the donor-acceptor distance RDA is the only fitting parameter to define the mean, the width, and the shape of E distribution. In practice, it often turns out that a single RDA is insufficient to describe FRET populations in PDA analysis. In these cases, it is convenient to assign a Gaussian distribution of donor-acceptor distances to each FRET population.4,7,21 The fit parameters are the mean distance 〈RDA〉 and the distribution half width, hw. This approach is also commonly used in the analysis of ensemble fluorescence decays.22,23 If all FRET states have similar total brightness (as assumed in this work), it is usually acceptable to use the same fluorescence distribution P(F) for all species.10 In the case of the Alexa488-Cy5 pair, this simplification is reasonable because there are no extreme variations in FRET, and the difference in the fluorescence quantum yields ΦF (ΦFD ) 0.8 and ΦFA ) 0.32) is partially compensated by a lower detection efficiency of the donor channel (green/red detection efficiency ratio is gG/ gR = 0.7), so that the term (gRΦFA)/(gGΦFD) amounts to 0.57. 2.2. Correlation between the Mean and the Apparent Width of Distance Distributions. In single-molecule fluorescence experiments on freely diffusing molecules, the FRET efficiency is usually calculated from donor and acceptor signals (eqs 2a and 2b)

E)

FA /ΦFA FD /ΦFD + FA /ΦFA

(2a)

with

FD )

FG SG - BG ) gG gG

and

FA )

SR - RFG - BR gR (2b)

In eq 2a, FD and FA are the corrected fluorescence intensities of the donor and the acceptor, respectively, and ΦFD and ΦFA denote corresponding fluorescence quantum yields. The fluorescence F is calculated from the measured signal S considering

(3)

Here, ΦFA is the position-sensitive acceptor fluorescence quantum yield, and R0r is the “reduced” Fo¨rster radius.24 R0r ) 9780 · [J(λ) · κ2 · n-4](1/6) [Å] ) 54 Å (for Alexa488-Cy5), with the DA spectral overlap integral J(λ), the orientation factor κ2, and the refractive index n. Equation 3 makes it clear that donor quenching does not change the FD/FA ratio and thus has no effect on calculated distances (eq 3). Let us now consider the case of acceptor quenching. We assume that the acceptor fluorophore exhibits a distribution of quantum yields which is not averaged out on the time scale of the diffusion time of FRET species (typically a few milliseconds). It is clear that even for a fixed DA distance, an apparent FRET efficiency distribution is then expected (eq 2a). Thus, the acceptor quantum yield distribution might be easily misinterpreted as an RDA distribution (eqs 2-3). If variations of FD/FA or E are formally attributed to a distance distribution with several apparent distances R˜(i), these distances can be calculated according to eq 3. It is then natural to use the same (mean) acceptor fluorescence quantum yield 〈ΦFA〉 for all states. As demonstrated in the Supporting Information (section 1), the apparent width of this distribution is correlated with the physical DA distance RDA, so that the presence of several appears acceptor states with corresponding quantum yields Φ(i) FA as several apparent DA distances R˜(i) (eq 4).

( )

R˜(i) ) RDA

〈ΦFA〉

1/6

(i) ΦFA

(4)

Equation 4 is easily obtained by rearranging eq 2a and taking 6 /R06)-1.25,26 Applying the rules into account that E ) (1 + RDA for error propagation for the function R˜(ΦFA) (eq 4), one obtains for the variance of the apparent DA distance var(R˜) 2 -1/6 var(R˜) ) RDA 〈ΦFA〉1/3var(ΦFA )

(5a)

-1/6 1/2 hw(R˜) ) RDA〈ΦFA〉1/6[var(ΦFA )]

(5b)

or

In other words, although the correlation between the DA distance RDA and the peak half width hw intuitively supports the flexibility hypothesis (bending of longer molecules produces broader distance distributions), such correlation could be also due to a simple photophysical artifact. Moreover, eq 5b states that the apparent distance distribution width due to acceptor quantum yield variations increases linearly with the mean DA distance, RDA, which is actually observed experimentally as reported in section 4.5. The FRET efficiency can also be calculated using the donor signal after acceptor bleaching,27 which, in principle, allows one to avoid the acceptor quantum yield problem. However, in experiments on freely diffusing molecules, this method is usually

Broadening of Single-Molecule FRET Efficiency Distributions not applicable. The effect of quantum yield variations on FRET in acceptor bleaching experiments is discussed in detail by Sabanayagam et al.27 2.3. Bias of 〈RDA〉. Assuming that extra distribution broadening is solely due to acceptor quantum yield variations, the mean of the Gaussian distribution used for PDA fits (〈RDA〉) is nothing else but the mean apparent distance 〈R˜〉 given by the individual apparent distances R˜(i) as computed by eq 4. From eq 4, it follows that 〈R˜〉 is not exactly equal to the physical DA distance RDA but is rather given by eq 6 -1/6 〈RDA〉 ) 〈R˜〉 ) RDA〈ΦFA〉1/6〈ΦFA 〉

(6)

Thus, as 〈ΦFA-1/6〉 > 〈ΦFA〉-1/6, there is a small bias toward longer distances. In practice, the correction factor 〈ΦFA〉1/6〈ΦFA-1/6〉 is often close to unity (for concrete numbers, see section 4.4). Moreover, when obtaining eq 6, we ignore the fact that with increasing acceptor brightness, FRET subpopulations become more likely to be selected by a burst search algorithm and/or fulfill a minimum photon number threshold in PDA (Smin). Therefore, species with apparently higher FRET efficiency are preferentially selected, which to some extent compensates for the bias of eq 6. This consideration is less relevant for low-FRET species because, in this case, the contribution of the red signal to the total fluorescence is small, and thus, the brightness of all species is similar. 3. Methods 3.1. Chemicals. Labeled DNA and RNA oligonucleotides were obtained from Purimex (Grebenstein, Germany). The NHS esters of Alexa488 (5-isomer) (Invitrogen), Alexa532 (Invitrogen), Alexa647 (Invitrogen), Atto647N (ATTO-TEC, Siegen, Germany), and Cy5 (GE-Healthcare) dyes were coupled via 5-C6-aminoallyldeoxythymidines. The DNA samples used in this work were fully complementary duplexes with either 66 or 22 base pairs. All DNA samples were internally labeled to avoid problems with dye sticking to DNA and the presence of multiple dye populations. The Cy5 and Alexa647 NHS esters contain sulfonic acid groups at the chromophore (two in the case of Cy5 and four in the case of Alexa647), so that sticking to the DNA is minimized.28 Depending on the sequence context, we observe interactions of Atto647N with the DNA (see below), which can be nicely detected by multiparameter fluorescence detection (MFD) (see below). A full list of DNA and RNA sequences and labeling positions referred to herein can be found in the Supporting Information. The measurements were performed at room temperature in a buffer with 20 mM Tris/HCl, 100 mM NaCl, 0.2 mM EDTA, and 0.4 mM ascorbic acid (pH 7.5). 3.2. Single-Molecule Fluorescence Measurements. Multiparameter fluorescence detection (MFD) measurements were performed as described in refs 24, 29, and 30. The fluorescent donor molecules (Alexa488 or Alexa532) were excited by a linearly polarized, active-mode-locked Argon ion laser (496.5 or 514.5 nm, respectively, 73.5 MHz, ∼300 ps). The laser light was focused into the dilute solution (640 nm) was used to reduce the contribution of scattered light. All measurements were performed at room temperature. 3.4. Simulations. Simulations were performed by using the Brownian dynamics approach36-38 as described.9,10,39 In addition, fluorescence decays were modeled as proposed by Chowdhury et al.40 using the experimental instrument response function (IRF) shape (full width at half-maximum (fwhm) ≈ 300-500 ps). Simulated data were saved in SPC132 format (Becker and Hickel, Germany) and analyzed in the same way as experimental data. 4. Results and Discussion 4.1. Broadening of E Distributions Observed for dsDNA Is Not Due to Structural Effects. 4.1.1. Analysis of the Donor Lifetime Distributions Using 2D Diagrams. The structure of double-stranded DNA (dsDNA) has been extensively studied by FRET on bulk samples and at the single-molecule level.28,41-44 Recently, extra broadening of FRET distributions obtained for labeled dsDNA molecules has been reported.4,7,11 We first attempted to demonstrate that in the case of dsDNA labeled with the Alexa488-Cy5 dye pair, apparent broadening of the FRET efficiency distribution is not related to any structural effect (RDA distribution or orientational effects). To detect subpopulations,45 we applied MFD, counted many single-molecules events, and analyzed the burst fluorescence lifetime, τD(A), of Alexa488 (donor) in the presence of FRET and compared it with E as calculated from donor and acceptor fluorescence intensities (eq 2a). It is clear that “real” RDA or R0

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distributions must be apparent in both intensity and lifetime distributions in a correlated manner.10,19 The expected E-τ D(A) dependence is given by eq 725

E)1-

τD(A) τD(0)

(7)

In eq 7, τD(0) is the donor lifetime in the absence of FRET. At this point, we do not explicitly distinguish between RDA distributions and orientational (κ2) effects (cf. ref 12) because both should lead to correlation between E and τD(A) (eq 7). Figure 1A shows the 2D histogram of E versus τD(A) obtained for dsDNA labeled with the Alexa488-Cy5 FRET pair (dsDNA1 sequence; see Supporting Information). The corresponding 1D parameter histograms are given as projections. Two major populations can be detected with respect to E, (I) donoronly (DOnly) at E ) 0 and (II) a FRET population centered at E ≈ 0.3. As demonstrated in ref 30, donor quenching is detected by the presence of several horizontally shifted populations. For our case, the histogram also reveals that two donor subpopulations exist for each major E population, (I) the major subpopulation, where the donor is unquenched (τD(0) ) 4.0 ns) and (II) a very small subpopulation of partially quenched donor with τD(0) ≈ 2.1 ns. At first glance, FRET subpopulations follow the expected E-τD(A) dependence (eq 7) if the individual τD(0) values are used (solid and dashed line). The E distribution of the major FRET population is significantly broader than expected for a shot noise limited distribution; assuming a Gaussian distance distribution, the PDA fit yields a mean distance 〈RDA〉 ) 61.6 Å, with a half width of hw ) 5.3 Å. Nevertheless, no correlation between E and τD(A) is observed within the FRET subpopulation. In other words, the broadened 2D E-τD(A) distribution has an approximately round shape, rather than oval, with its long axis parallel to the theoretical FRET line (solid line in Figure 1A, eq 7). According to eq 3, no broadening of intensities is to be expected. To illustrate the E-τD(A) correlation that should arise from a RDA or R0 distribution in such FRET experiments, we performed a simulation of a MFD experiment for the major FRET population equivalent to that shown in Figure 1A. We assumed a Gaussian RDA distribution with 〈RDA〉 ) 61.6 Å and hw ) 5.3 Å, as obtained experimentally. The simulation closely mimics experimental photon statistics, with the brightness of the “molecules”, background, mean burst size, diffusion time, and other relevant parameters reproducing experimental values within (3%. The simulated data in Figure 1B clearly show a correlated E-τD(A) 2D distribution as expected by eq 7 (i.e., oval shape; long axis approximately parallel to the theoretical E-τD(A) dependence). The absence of such correlation in the experimental data (Figure 1A) strongly suggests that broadening of the E distribution is not due to a distribution of DA distances. The E and τD(A) distributions are also uncorrelated when the Alexa488-Alexa647 FRET pair is used (Figure 1C). For the same dsDNA sequence labeled with the Alexa532Atto647N FRET pair, the situation is different (Figure 1D). At least two FRET states are clearly visible, which follow the expected E-τD(A) dependence (eq 7), indicating a distribution of RDA (or alternatively R0). A similar FRET pattern is observed for dsDNA labeled with the Alexa488-Atto647N pair. We attribute the presence of two populations to another type of dye artifact (for instance, the Atto647N dye sticking to DNA; cf. refs 46 and 47), which is impossible to distinguish from a distance distribution that could occur due to flexibility of the dsDNA molecule.

Figure 1. 2D probability histograms of FRET efficiency E (eq 2a) versus the donor lifetime τD(A). The number of molecules (fluorescent bursts) in each bin is in gray scale, shaded from white (lowest) to black (highest). The following data sets are shown: (A) Experimental data obtained for dsDNA labeled with Alexa488 and Cy5 (dsDNA1), separated by 15 base pairs. PDA fit yields 〈RDA〉 ) 61.6 Å and hw ) 5.3 Å. (B) Simulated data mimicking the FRET population shown in subplot (A). A Gaussian distribution of DA distances with 〈RDA〉 ) 61.6 Å and hw ) 5.3 Å (approximated by 12 discrete states) is simulated. (C) Experimental data obtained for dsDNA6 labeled with Alexa488 and Alexa647. (D) Experimental data obtained for dsDNA1 labeled with Alexa532 and Atto647N. In all plots, solid lines indicate the E versus τD(A) dependence given by eq 7; the dashed line in (A) shows the same dependence calculated for the partially quenched donor subpopulation with τD(0) = 2.1 ns.

To conclude, only a correlated broadening of E and τD(A) distributions in the 2D E-τD(A) diagrams suggests a FRET effect according to eq 7. Uncorrelated broadening (Figure 1A and C) indicates heterogeneities in D and A environments resulting in different fluorescence quantum yields. 4.1.2. Comparison between Various dsDNA Sequences and ssDNA. Further evidence against the “flexibility” hypothesis can be obtained by comparing the FRET distributions of ssDNA and dsDNA labeled with Alexa488 and Cy5. Unlike dsDNA, ssDNA is believed to be rather flexible in solution,48 with no residual structure, so that complete averaging takes place on the millisecond time scale. By using PDA, we compared FRET efficiency distributions measured for dsDNA and ssDNA with comparable mean DA distances. Surprisingly, very similar distance distribution widths were obtained for ssDNA and dsDNA molecules (Table 1). Moreover, we compared the apparent width of RDA distributions of several dsDNA sequences with various contents of GC base pairs. Although a significant difference in the flexibility of these DNA fragments is expected,49-52 no sequence effect on the distribution width was found by PDA (Table 1). The data summarized in Table 1 show a surprising result. Provided that the 〈RDA〉 values are comparable, similar distance distribution widths are measured for molecules of completely different structure. This fact indicates that the observed broadening cannot be strongly related to a static heterogeneity in structure but rather to a moleculeindependent dye artifact. It is likely that the heterogeneity due

Broadening of Single-Molecule FRET Efficiency Distributions TABLE 1: Comparison of Apparent DA Distance Distribution Width Obtained for Various dsDNA and ssDNA Sequences Labelled with Alexa488 and Cy5a sample

〈RDA〉 [Å]

hw [Å]

dsDNA2 ssDNA7 (poly-T) dsDNA3 (GC-rich) dsDNA4 (AT-rich)

70.3 ( 0.7 69.7 ( 0.9 70.8 ( 0.4 71.3 ( 0.4

5.0 ( 0.3 4.6 ( 0.4 5.6 ( 0.4 5.0 ( 0.3

a The values were determined by PDA with a time window of 1 ms. Refer to SI Table 1 for the sequence of each sample.

to flexibility and structural dynamics must be averaged out on a millisecond time scale (see below). 4.2. Experimental Artifacts Contributing to the Width of FRET Distributions. Several possible explanations for broadening of FRET distributions beyond shot noise limits have been proposed.4,7,11 We discuss the major possible sources of broadening and their likely effect on our data in the sections below. 4.2.1. Optical Artifacts and Photophysical Processes, Which Are Fast with Respect to the Dwell Time of the Molecule. Size and position mismatch of donor and acceptor detection volumes produces a distribution of the detection efficiency ratio4,7 and might thereby contribute to the E distribution width. In our case, this explanation seems to be unlikely because (i) shot noise limited distributions are obtained in control experiments with dye solutions,4 (ii) fluorescence correlation spectroscopy (FCS) shows very similar diffusion times for green and red dyes,4 and (iii) hw values are very reproducible over time. Triplet formation or, equivalently, any other fast blinking process, such as cis-trans isomerization of Cy528,53 at optical saturation conditions, might also contribute to the E distribution width.11 Although these processes are fast compared to the diffusion through the laser focus, inhomogeneous spatial distribution of the donor/acceptor brightness ratio is created due to the spatial dependent saturation effects of the Gaussian-shaped excitation intensity profile.54 Obviously, the extent of broadening due to triplet states depends on the excitation power. Another side effect of saturation is a strong correlation between the minimum photon number threshold (Smin) and the mean FRET efficiency, as could be shown by simulations. None of these effects is observed in our measurements on dsDNA (for details, see, Supporting Information S.Figure 1). We conclude that at least at moderate excitation power, triplet formation and cis-trans isomerization of Cy5 have no significant effect on the FRET distribution width, as demonstrated for labeled dsDNA2 sample (Supporting Information S.Figure 1). 4.2.2. Bleaching and Blinking of the Acceptor Dye, Which Is Slow or Comparable to the Dwell Time of the Molecule. In experiments on immobilized molecules, blinking of the acceptor dye is considered to be a major problem55,56 However, the reported Cy5 blinking is typically slow on the millisecond time scale,55-58 and FRET species with Cy5 in a dark state are expected to behave as DOnly molecules. Blinking or bleaching of the acceptor dye on the millisecond time scale would appear as FRET dynamics, which is not observed for labeled dsDNA (Supporting Information S.Figure 2). To gain a better understanding of blinking and bleaching of Cy5 and its effects on FRET, we performed fluorescence correlation spectroscopy (FCS) experiments on labeled dsDNA at different excitation intensities. In Figure 2A, donor and acceptor fluorescence normalized by the molecule number, Fcpm (counts per molecule), is plotted versus the excitation irradiance. It is clear that the acceptor signal saturates at much lower

J. Phys. Chem. B, Vol. 114, No. 18, 2010 6201 intensities than the donor signal. These findings are consistent with previously published results.32,59 In addition, FCS allows one to determine the total number of green and red molecules in the detection volume.60 FCS results shown in Figure 2B indicate that compared to donor molecules (open triangles), at high excitation power, a significant fraction of acceptors enter dark states even before reaching the observation volume (open circles). Blinking and/or bleaching of Cy5 is largely suppressed in the presence of Trolox (saturated aqueous solution, ∼1 mM)55,61 (Figure 2). Trolox helps to restore the red signal (Figure 2A, full circles), which is mainly due to an increased number of active acceptors reaching the excitation volume (Figure 2B, full circles). Despite having a strong effect on Cy5 blinking, Trolox showed no significant influence on the width of FRET distributions (see Supporting Information S.Figure 3). Taken together, our results confirm that blinking of Cy5 appears mainly as an increase of the apparent DOnly fraction and has a negligible effect on the width of E distributions. 4.2.3. Heterogeneous Properties of Fluorophores. Dye artifacts may include donor and acceptor quenching and variations of the Fo¨rster radius, R0.4,10,27 However, donor dye quenching competes with FRET and therefore does not affect the calculation of E and RDA (see eq 3), and variations of R0 produce an E-τD(A) correlation (eq 7) similar to that shown in Figure 1D. Thus, we focused our attention on the acceptor dye properties. In the case of Cy5, bulk fluorescence lifetime measurements indicate the presence of multiple states if the dye is conjugated to a macromolecule (see also section 4.3 and ref 62). In particular, Cy5 bound to dsDNA exhibits a doubleexponential fluorescence decay with τ1 ) 0.98 ns (83%), τ2 ) 2.1 ns (17%), and χr2 ) 1.36, whereas a single-exponential fit yields χr2 ) 49.6 (Supporting Information S.Figure 4). In contrast, the fluorescence relaxation of Cy5 in water is welldescribed by a single-exponential decay (τ ) 0.90 ns, χ2r ) 1.24). However, nonexponential fluorescence decay of dsDNA-Cy5 does not necessarily imply the existence of multiple states on a millisecond time scale; one could argue that multiple dye states might interconvert much faster and therefore should have no effect on the width of intensity-based FRET histograms. To answer this question, we analyzed the burst lifetime distribution of directly excited Cy5 bound to dsDNA, in comparison with that of the free Cy5 dye, as described in the next section. 4.3. Multiple States of Cy5 Are Stable on a Millisecond Time Scale. The exact shape of a burst lifetime distribution is rather difficult to predict because of the complex behavior of the maximum likelihood estimator (MLE), which is typically used for lifetime analysis of single-molecule data.63-65 Therefore, we compared experimental burst lifetime distributions with simulated data. The validity of such a comparison was first tested on the MFD data collected from dye solutions in water. Simulations closely resemble experimental conditions, taking experimentally determined brightness (Q) and the diffusion time (td) of the molecules and the IRF shape as input parameters. Simulated data were analyzed using exactly the same burst selection criteria as those applied to the experimental data. Figure 3A and B shows the experimental and simulated burst lifetime distributions of directly excited free Rhodamine 110 (Rh110) and Cy5, respectively. For the case of Rh110, the width of the burst lifetime distribution is reproduced with an accuracy of 2% (Figure 3A). For Cy5 measurements, the emission was detected with a different type of avalanche photodiode (see experimental); these detectors exhibit some IRF drift with count rate,66 which may explain a slight extra broadening (∼10-15%) of the Cy5 lifetime distribution (Figure 3B). On the other hand,

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Figure 2. (A) Signal (counts per molecule Fcpm) and (B) number of molecules as determined by FCS, as a function of the mean excitation irradiance. Data are shown for the green (donor) signal (open triangles) and the red (acceptor) signal in the absence of Trolox (open circles) and the red signal in the presence of Trolox (full circles). The signal in (A) represents the measured count rate divided by the number of molecules measured for the same sample at the lowest intensity. The number of molecules is calculated from the correlation amplitude and normalized relative to the number of molecules obtained at the lowest intensity. For the given focal geometry, the mean irradiance of 10 kW/cm2 corresponds to ∼80 µW at the objective.

Figure 3. Comparison between experimental (gray areas) and simulated (solid black lines) burst lifetime distributions, presented for (A) Rh110 in water (Q ) 59.5 kHz; td ) 0.26 ms), (B) Cy5 in water (Q ) 25.8 kHz; td ) 0.5 ms), and (C) dsDNA1 labeled with Cy5 (Q ) 13.8 kHz; td ) 3 ms). Cy5 is excited directly at λex ) 635 nm. (D-F) 2D probability histograms of anisotropy r versus the lifetime τD(A) or τA, generated for (D) donor anisotropy calculated from the data of Figure 1 A, (E) Cy5 in water, and (F) dsDNA1 labeled with Cy5. The solid lines show the theoretical dependence of r on τ given by the Perrin equation r ) r0/(1 + τ/F). The values of F are shown in each plot, r0 ) 0.385.

the burst lifetime distribution of dsDNA-Cy5 is significantly broader (∼80%) than the simulated one (Figure 3C). The most likely explanation is that distinct local quenching takes place in dsDNA1-Cy5, which leads to a distribution of lifetime and quantum yield states. What is more important for PDA is that these states are stable over the burst duration, that is, on a millisecond time scale. This means that quenching of Cy5 contributes to the broadening of E distributions (eqs 2-5a). The fact that two distinct peaks at ∼1 and 2 ns are not observed (Figure 3C) can be due to a significant width of both peaks and/or a complex distribution of lifetimes that cannot be resolved by TCSPC (see section 4.4). In addition, we performed the fluorescence intensity distribution analysis (FIDA)38 of dsDNA1-Cy5 and Cy5 in water using time windows of 40 µs. As expected, a single brightness is sufficient to describe the intensity distribution of free Cy5 (χr2 ) 0.78). In agreement with TCSPC data and burst lifetime analysis on the single-molecule level, FIDA indicates that for dsDNA1-Cy5, at least two Cy5 states with different quantum yields are present. A fit with a single state fails with χr2 ) 253, whereas introduction of the second state improves the fit

significantly (χr2 ) 8.5). At a given excitation intensity, the brightness values are Q1 ) 12.4 kHz (81%) and Q2 ) 38.6 kHz (19%). In order to determine whether these Cy5 states interconvert on a microsecond to millisecond time scale, we performed dynamic PDA67 and fluorescence lifetime-filtered FCS (FLCS) analysis.39,62,68-70 PDA of dsDNA FRET data indicates that the same static model can be fitted to experimental FRET distributions irrespective of the time window length (0.5, 1, and 2 ms; see Supporting Information S.Figure 2). This would be impossible if any FRET dynamics on a millisecond time scale were present.67 In agreement with dynamic PDA, the species crosscorrelation function (SCCF) calculated using FLCS shows no species interconversion dynamics (i.e., no anticorrelation) on the microsecond to millisecond range (Supporting Information S.Figure 5). Although one could argue that a very small anticorrelation term in the microsecond region is visible in SCCF, it cannot be attributed to complete and direct species interconversion because in that case, SCCF drops to a baseline value of 1 at short correlation times.39 Taken together, these results again indicate that two or more Cy5 states are stable on

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Figure 4. PDA of dsDNA2 labeled with the Alexa488-Cy5 pair, separated by 21 base pairs. (A) Experimental SG/SR histogram fitted assuming RDA ) 71.6 Å (dashed red line; χr2 ) 5.4) and a Gaussian distribution of DA distances (〈RDA〉 ) 70.3 Å, hw ) 5.0 Å). Both models include also (1) (2) /ΦFA is set to be equal to the lifetime ratio (0.47) and the fractions of a DOnly population (30 and 23%, respectively). (B) PDA fit for which ΦFA FRET states correspond to TCSPC species amplitudes (83 and 17%, respectively); 26% DOnly; χr2 ) 1.33. RDA ) 68.7 Å is obtained as the only FRET-related fit parameter. Vertical dashed lines indicate SG/SR ratios corresponding to R1, R2, and DOnly. PDA parameters: BG ) 1.66 kHz; BR ) 0.64 kHz; crosstalk ) 0.019; time window ) 1 ms; R0 ) 52 Å.

at least the millisecond time scale, which would lead to an apparent distribution of FRET efficiencies (eq 5). Gregor and Enderlein previously studied Cy5 state dynamics in a Cy5-protein complex62 and observed some fast (µs) interconversion between the dye states. However, the authors found also that the interconversion rate is determined by the microenvironment (i.e., not observed for free Cy5) and probably by the excitation power,62 which means that Cy5 might behave differently if conjugated to dsDNA. Other fluorophores also show distributions of lifetimes and quantum yields, which is in fact not unusual and not specific to the cyanine family. For example, for Alexa488 bound to macromolecules, the presence of two stable species with fluorescence lifetimes of 4.1 and ∼2 ns is often obvious71 (also visible in Figures 1A and 3D). Klenerman et al. showed that Alexa647, structurally nearly identical to Cy5, exists in at least three states.72 Sauer and coworkers recently studied the Atto647N dye and found a distribution of various fluorescence parameters (M. Sauer et al., personal communication). Thus, the problem is not unique to Cy5, may often contribute to E distributions, and must be taken into account. Multiple bright states of Alexa488 and Cy5 attached to dsDNA are clearly resolved in 2D histograms of the polarization anisotropy (r) versus lifetime (Figure 3D-F). Dye or FRET subpopulations are expected to approximately follow the Perrin equation r ) r0/(1 + τ/F),24,73 where r0 is the fundamental anisotropy and F is the mean rotational correlation time. For example, in Figure 3D, we analyzed the donor anisotropy of the sample dsDNA1 labeled with Alexa488 and Cy5, which has been already analyzed for FRET in Figure 1A. Several populations of dsDNA1 are visible, DOnly, FRET, and partially quenched DOnly and FRET species (cf. Figure 1A), which all have the same mean correlation time. In contrast, free Cy5 in water shows a single uncorrelated peak in a rA-τA 2D distribution, which is consistent with the narrow burst lifetime distribution presented in Figure 3B. However, in the case of dsDNA-Cy5, the rA-τA distribution is asymmetric with a positive correlation between rA and τΑ (Figure 3F). According to the Perrin equation, this correlation is unexpected. To conclude, the broadening of fluorescence lifetime and anisotropy consistently indicates that multiple microenvironments are accessible to Cy5 when it is coupled to DNA. The individual states are stable over the burst duration (Figure 3F). 4.4. Modeling Multiple Acceptor States in PDA. Previously, we demonstrated that in PDA it is usually difficult to distinguish between a Gaussian distribution of distances and several discrete states.10 Thus, an introduction of two apparent

FRET efficiencies for each RDA (cf. eqs 2-5a) could very well explain the need to fit a Gaussian distance distribution to experimental FRET peaks. Figure 4 shows the experimental SG/SR distribution and PDA of dsDNA2 labeled with Alexa488 and Cy5 separated by 21 bp. This low-FRET sample exhibits the broadest apparent distance distribution width (see also section 4.5). The SG/SR distribution cannot be fitted with a single FRET state (RDA ) 68.9 Å; χ2r ) 5.3) (red line in Figure 4A); an apparent Gaussian distance distribution with 〈RDA〉 ) 70.3 Å and hw ) 5.0 Å fits the data much better (χr2 ) 0.8, full black line). Alternatively, there are a number of ways that one can fit the signal distribution by two FRET states. One possibility involves a free fit to two FRET states, which yields R1 ) 71.2 Å (60%), R2 ) 62.2 Å (14%), and 26% of DOnly with χr2 ) 1.14, that is, this model is sufficient to explain extra broadening of the experimental SG/SR distribution. It should be noted that the obtained relative fractions of FRET subpopulations (81 and 19%) are very similar to fluorescence decay amplitudes measured by TCSPC (83 and 17%, respectively) as well as to the fractions of Cy5 states recovered by FIDA (81 and 19%). Considering eq 4 and assuming that R1 and R2 populations correspond to the same physical RDA (being actually R˜(1) and (1) R˜(2) in eq 4) but different acceptor quantum yield states (ΦFA (2) (1) (2) and ΦFA), one calculates ΦFA/ΦFA ) 0.44. This is very similar to the lifetime ratio of τ1/τ2 ) 0.47 obtained by ensemble TCSPC. All of these findings are consistent with the idea of local dynamic quenching of Cy5, for which it is expected that Φ(i) is proportional to τi and the fractions of the states are equal FA to the corresponding lifetime amplitudes.25 This finding motivates a second approach to PDA fitting using several predefined parameters. Φ(1) /Φ(2) is set to be equal to the lifetime ratio, and FA FA the fractions correspond to TCSPC species amplitudes. Now, an acceptable fit with χr2 ) 1.33 is obtained for only one free FRET parameter (Figure 4B), the physical DA distance RDA ) 68.7 Å. This PDA fit, although including two FRET states, needs only one free FRET parameter (i.e., unlike the Gaussian distribution model, it does not include the apparent hw as a variable). For this solution, it is possible to calculate (eq 4) the apparent distances R˜(1) ) 70.8 Å and R˜(2) ) 62.3 Å, which are very similar to the values obtained in the unconstrained fit. We also note that for the reasons discussed in section 2.3 (eq 6), RDA ) 68.7 Å obtained using the latter approach is smaller than 〈RDA〉 ) 70.3 Å of a Gaussian fit. The difference is about 2%, while eq 6 predicts a correction factor 〈ΦFA〉1/6 〈ΦFA-1/6〉 of 1.01. Considering that very different distance distribu-

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Figure 5. Mean donor-acceptor distances 〈RDA〉 and the apparent distance distribution half widths (hw) measured for a series of labeled dsDNA and dsRNA fragments. The dsDNA sequence dsDNA5 was labeled with the Alexa488-Cy5 FRET pair at various positions, providing a separation of 5-27 base pairs between the dyes (black squares). The dsRNA sequence dsRNA1 was labeled with the Alexa488-Cy5 FRET pair at various positions, providing separations of 16-22 base pairs between the dyes (open circles). 〈RDA〉 and hw values are obtained by PDA using BG ) 2.2 kHz, BR ) 0.9 kHz, crosstalk ) 0.009, time window ) 1 ms, and R0 ) 52 Å. Error bars represent confidence intervals calculated from 〈RDA〉 - hw χ2-surfaces21 (for RNA data, error bars are comparable to the symbol size). The straight lines show linear approximations of the experimental data according to eq 5b, with offsets very close to the theoretically expected value of zero, hw ) 0.076〈RDA〉 - 0.16 Å for dsDNA (solid line) and hw ) 0.044〈RDA〉 - 0.29 Å for dsRNA (dashed line).

tion shapes (Gaussian versus two states) are used to fit the data, a better agreement between these values is not expected. The proposed correction of the PDA model function which makes use of bulk TCSPC data is based on several approximations. First, we assume no interconversion between the states, which is reasonable, at least at moderate excitation power (see section 4.3 and SCCF, Supporting Information S.Figure 5). The assumption that the quantum yield is proportional to the lifetime is also critical but might become violated at higher excitation intensities due to different saturation behavior of the acceptor subpopulations. Moreover, ensemble lifetime measurements do not resolve, but also cannot exclude, the presence of three or more lifetimes (see also Supporting Information S.Figure 4E). For example, a three-state model with one Cy5 lifetime fixed at 1.3 ns fits well both to TCSPC and smFRET data (Supporting Information S.Figure 6). In the case of PDA, this model has only one free parameter, RDA, and all other parameters are obtained from bulk TCSPC data. The fact that this model approximates the data most accurately (Supporting Information S.Figure 6) might indeed indicate the presence of more than two components, which simply cannot be resolved by bulk TCSPC. As an alternative to the proposed correction method, a reference FRET measurement on a rigid molecule could be utilized to determine minimal broadening due to complex acceptor photophysics. As shown in the next section, the apparent broadening hw constitutes a constant fraction of 〈RDA〉, which can be calculated from a few calibration FRET measurements. 4.5. Apparent RDA-hw Correlation. As discussed in section 2.2, a correlation between the mean distance and the apparent distribution width is expected as a consequence of the acceptor quantum yield distribution (eq 5). To demonstrate this behavior experimentally, we reanalyzed FRET data obtained for a series of dsDNA molecules labeled with the Alexa488-Cy5 pair.44 The separation between the dyes varied between 5 and 27 base pairs. In Figure 5, the apparent distance distribution half width (hw) is plotted versus 〈RDA〉, which is close to the physical distance RDA (eq 6) for the analyzed distributions. A linear

Kalinin et al. dependence of hw on 〈RDA〉 is clearly observed. The straight line in Figure 5 represents a linear fit to the experimental 〈RDA〉-hw dependence, given by hw ) (0.076 ( 0.012)〈RDA〉 - (0.16 ( 0.68 Å). The linear fit function essentially crosses the origin, indicating no significant distance-independent broadening (for example, RDA distribution due to dye sticking). The expected slope of the 〈RDA〉-hw dependence, if due to the acceptor photophysics, can be estimated by eq 5. The lifetime distribution of Cy5 can be recovered by the maximum entropy method (MEM)74-77 (the analysis of the fluorescence decays is demonstrated in Supporting Information S.Figure 4E,F). As(i) ∝ τ and 〈ΦFA〉 ) 0.32,44 all parameters in eq suming that ΦFA 5 are easily calculated. Depending on the weight of the entropy factor (Supporting Information S.Figure 4E,F), the calculated -1/6 1/2 )] ) for the relation 〈RDA〉-hw is slope (〈ΦFA〉1/6[var(ΦFA between 0.052 and 0.064, which is in a good agreement with the experimental value of 0.076 ( 0.012. This result confirms that the distribution of the acceptor quantum yields, if completely static on a millisecond time scale, can largely explain the observed broadening of our FRET distributions. In addition to dsDNA data, we reanalyzed a few FRET measurements of dsRNA. A single RNA sequence, dsRNA1, is labeled with Cy5 at the same position and with Alexa488 at three different positions (sequences and labeling positions can be found in the Supporting Information). The fluorescence decay of directly excited Cy5-dsRNA1 is biexponential, with two relatively similar components, 0.84 (53%) and 1.3 ns (47%), which is significantly different from a typical fluorescence relaxation of Cy5 in dsDNA (section 4.3). According to eq 5, for dsRNA samples showing less variation of the acceptor quantum yields, narrower apparent distance distributions are expected. The experimental 〈RDA〉-hw dependence for dsRNA presented in Figure 5 (open circles) clearly supports this prediction. A linear fit to the data is best described as hw ) 0.044〈RDA〉 - 0.29 Å. By using MEM, a theoretical slope of ∼0.04 (eq 5) can be estimated, which is very similar to the experimental value. As in the case of dsDNA, the distanceindependent contribution to hw (-0.29 Å) is small, indicating negligible dye sticking. Recently, an X-ray scattering study of dsDNA flexibility has been published.16 For a series of dsDNA oligonucleotides, the authors report unusually broad end-to-end distance distributions, with absolute distribution widths comparable to those presented in Figure 5. It is also interesting to note that according to ref 16, a quadratic dependence of the end-to-end distance distribution variance on 〈R〉 (i.e., linear hw-〈R〉 dependence) is observed (cf. Figure 5). On the other hand, the authors do not dispute the common view of the time scale of dsDNA chain dynamics. With respect to this work, we believe that sufficient evidence exists (section 4.1) to conclude that effects discussed in ref 16 do not significantly contribute to the observed FRET distributions measured with millisecond time resolution because these fluctuations occur on a much faster time scale. 5. Concluding Remarks We have shown that an apparent FRET efficiency distribution may reflect acceptor dye properties, rather than a DA distance distribution, even in experiments on freely diffusing molecules. The minimal possible width is not that predicted by the PDA theory but is determined by variations of the acceptor fluorescence quantum yield. As the acceptor photophysics problem cannot be easily avoided, we suggest a set of tools to analyze the reasons for broadened FRET distributions. At first, MFD allows one to check whether the observed broadening is due to

Broadening of Single-Molecule FRET Efficiency Distributions distinct acceptor brightnesses or indicates a structurally relevant effect. If an individual FRET distribution in 2D shows a E-τD(A) correlation (oval shape, long axis follows eq 7), this indicates static or dynamic heterogeneity within this population. Moreover, an overall correlation between the FRET efficiencies calculated using intensities (eq 2) and donor lifetimes (eq 7) is expected. As a second option, PDA analysis allows for a good fit of experimental E distributions if a single fixed donor-acceptor distance is assumed and multiple acceptor states are taken into account, which are defined by distinct fluorescence lifetimes. In a third type of experiment, we recommend calibrating the FRET pair with a rigid (or very flexible) molecule to clearly attribute extra broadening to a FRET-related effect. As a final check, we provide a simple theory based on the linear correlation between the DA distance half width (hw) and the DA distance RDA (eq 5), which allows one to estimate whether the acceptor photophysics is the only factor that contributes to extra broadening. If a set of related molecules with similar dye environments and distinct DA distances can be studied, one can check whether the slope of the hw-RDA relation is close to the value given by a quasi-static acceptor fluorescence quantum yield (or lifetime) distribution or whether the slope is significantly higher or specific outliers can be detected. In conclusion, accounting for multiple acceptor states is sufficient to explain the observed broadening of experimental FRET distributions for the dsDNA studied in this work. Acknowledgment. C.A.M.S. and S.K. thank the German Science foundation (DFG) in the priority program SPP 1258 “Sensory and regulatory RNAs in prokaryotes” for funding this work. S.K. is also grateful to the Alexander von Humboldt Foundation for financial support. E.S. was funded by the Swedish foundation STINT. S.W.M. was supported by the EU Marie Curie Actions Research Training Networks “DNA enzymes”. We thank M. Schmitz for helping to design the DNA sequences. We are grateful to Jerker Widengren for the very fruitful collaboration within the Swedish foundation STINT exchange program. We thank Peter Karageorgiev, Volodymyr Kudryavtsev, and Don Lamb for valuable discussions. Finally, we are grateful to Anna Woz´niak, Filipp Oesterhelt, and Simon Sindbert for giving us an opportunity to reanalyze their experimental data (section 4.5). Supporting Information Available: Derivation of eq 4, DNA and RNA sample information, and additional results. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Weiss, S. Science 1999, 283, 1676. (2) Roy, R.; Hohng, S.; Ha, T. Nat. Methods 2008, 5, 507. (3) Chung, H. S.; Louis, J. M.; Eaton, W. A. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 11837. (4) Antonik, M.; Felekyan, S.; Gaiduk, A.; Seidel, C. A. M. J. Phys. Chem. B 2006, 110, 6970. (5) Gopich, I.; Szabo, A. J. Chem. Phys. 2005; 014707. (6) Gopich, I. V.; Szabo, A. J. Phys. Chem. B 2007, 111, 12925. (7) Nir, E.; Michalet, X.; Hamadani, K. M.; Laurence, T. A.; Neuhauser, D.; Kovchegov, Y.; Weiss, S. J. Phys. Chem. B 2006, 110, 22103. (8) Gopich, I. V.; Szabo, A. J. Phys. Chem. B 2009, 113, 10965. (9) Kalinin, S.; Felekyan, S.; Antonik, M.; Seidel, C. A. M. J. Phys. Chem. B 2007, 111, 10253. (10) Kalinin, S.; Felekyan, S.; Valeri, A.; Seidel, C. A. M. J. Phys. Chem. B 2008, 112, 8361. (11) Vogelsang, J.; Doose, S.; Sauer, M.; Tinnefeld, P. Anal. Chem. 2007, 79, 7367. (12) Cherny, D. I.; Eperon, I. C.; Bagshaw, C. R. Eur. Biophys. J. 2009, 38, 395.

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