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FRET or No FRET: A Quantitative Comparison

BioMicroMetrics Group, Laboratory for Biomechanics, Swiss Federal Institute of Technology, CH-8952 Schlieren, Switzerland

Correspondence: Address reprint requests to Claude Berney, Tel.: +41-1-633-6152; Fax: +41-1-633-1124; E-mail: berney{at}biomech.mavt.ethz.ch.

	ABSTRACT

TOP ABSTRACT INTRODUCTION FRET EFFICIENCY AND INDEX... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Fluorescence resonance energy transfer (FRET) is a technique used to measure the interaction between two molecules labeled with two different fluorophores (the donor and the acceptor) by the transfer of energy from the excited donor to the acceptor. In biological applications, this technique has become popular to qualitatively map protein-protein interactions, and in biophysical projects it is used as a quantitative measure for distances between a single donor and acceptor molecule. Numerous approaches can be found in the literature to quantify and map FRET, but the measures they provide are often difficult to interpret. We propose here a quantitative comparison of these methods by using a surface FRET system with controlled amounts of donor and acceptor fluorophores and controlled distances between them. We support the system with a Monte Carlo simulation of FRET, which provides reference values for the FRET efficiency under various experimental conditions. We validate a representative set of FRET efficiencies and indices calculated from the different methods with different experimental settings. Finally, we test their sensitivity and draw conclusions for the preparation of FRET experiments in more complex and less-controlled systems.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION FRET EFFICIENCY AND INDEX... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Förster resonance energy transfer (FRET) is a process by which a fluorophore (the donor) in an excited state transfers its energy to a neighboring molecule (the acceptor) by nonradiative dipole-dipole interaction (Förster, 1948; Lakowicz, 1999). Although not necessary, in most cases the acceptor is also a fluorescent dye. In this case, FRET also stands for fluorescence resonance energy transfer.

In steady-state FRET microscopy, two different approaches are generally used to measure FRET: 1), Emission measurement. Excitation of the donor and detection of the light emitted by either the donor and/or the acceptor in the presence of the other fluorophore. When FRET occurs, the donor emission is decreased and the acceptor emission is increased. 2), Acceptor photobleaching. Excitation of the donor and detection of the light it emits before and after acceptor photobleaching. In both approaches, values can be obtained that represent either a FRET index or the transfer efficiency.

A FRET index is a relative value that varies with changes in energy transfer associated with changes in the donor-acceptor configuration. It should increase when FRET increases, and should decrease when FRET decreases. FRET indices are useful to perform qualitative studies or to take relative measures within the same experiment. However, each FRET index is tuned for specific related experimental needs. A direct comparison between results obtained with different indices can be difficult.

On the contrary, the transfer efficiency (E) is a direct measure of the fraction of photon energy absorbed by the donor that is transferred to an acceptor. It can be calculated as the ratio of the transfer rate k_T to the total decay rate of the donor where _D is the lifetime of the donor in the absence of acceptors or any other quenching effects. It can also be measured as the relative fluorescence of the donor in presence (F_DA) and absence (F_D) of the acceptor E = 1 - F_DA/F_D or from the lifetimes under these respective conditions E = 1 - _DA/_D (Lakowicz, 1999). Since E depends on the inverse of the sixth power of the distance r between the two fluorophores, FRET has become the technique of choice to observe protein-protein interaction and to measure distances between fluorophores (Stryer, 1978; Clegg, 1996). R₀ is known as the Förster distance and represents a characteristic parameter of every dye pair defining the distance at which the efficiency is 50%.

As with any proper fluorescence measurement to be quantitative, FRET methods have to account for biases due to 1), bleed-through in excitation, i.e., when a donor is excited by the acceptor's excitation wavelength and vice versa; and 2), cross talk in emission detection, i.e., when the emission of a donor also contributes to the signal measured in a setup for acceptor detection, and vice versa. It is often difficult to separate the contribution of direct cross talk from the contribution of bleed-through signals. We therefore use the term "cross talk" to refer to both kinds of artifacts for the rest of this article.

Various methods introducing different observation strategies for FRET efficiency and indices can be found in the literature. The purpose of the presented work is to validate their performance under various experimental conditions. We have implemented an experimental FRET system, which permits a free selection of the pair and where the donor and acceptor concentrations as well as the average distance between donor and acceptor can be controlled. The system relies on a surface monolayer of biotinylated poly-(L)-lysine-graft-poly-ethylene-glycol (PLL-g-PEG-biotin). This defines a 2D distribution of fluorophores, which can be stochastically modeled. Reference FRET values for the comparison of the analyzed methods are generated by Monte Carlo simulations (MCS) of the transfer process. The simulation accounts for the dynamics and competition in transfer, characteristic for a multi-donor and multi-acceptor system, and considers the kinetics of excitation and relaxation of the fluorophores. Experimental data obtained from microscopy of the surface system are used to calculate the various FRET efficiencies and FRET indices. All the geometric parameters as well as the dye pairs have been varied to test the methods under different conditions. These results are compared with the MCS to determine the sensitivity, biases and uncertainty of each method. We conclude with a practical and objective guide to steady-state FRET microscopy including a few warning about some of the most widespread observation strategies.

	FRET EFFICIENCY AND INDEX METHODS

TOP ABSTRACT INTRODUCTION FRET EFFICIENCY AND INDEX... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Various methods have been reported to quantify FRET from measured changes in donor and acceptor emission. Table 1 summarizes methods that yield a measure of FRET efficiency and Table 2 those that derive FRET indices, along with examples of applications they were used in. Note that several methods were originally used in flow cytometry (FC) or spectroscopy (S). All of them can, however, be implemented in microscopy (M). The methods are classified according to the number of filter sets necessary, the number of samples and images required, and the level of correction involved. Our notation is largely inspired by the one proposed by Gordon et al. (1998) (see Materials and Methods for further explanations).

In contrast to method E₁, which is calculated from a ratio of signal originating from two different samples (d and b), the methods E₂–E₇ all rely on the signal directly obtained in the FRET channel (F) in presence of both fluorophores (b). The methods vary in their schemes for cross talk correction. Method E₂ requires prior knowledge of dye concentration and absorption coefficients. It is assumed that the acceptor is not excited at the donor excitation wavelength, and that there is no cross talk of the acceptor in the donor channel. The same assumptions are applied to method E₃, but for the donor. The advantage of these two methods over method E₁ is that they only require one sample where both fluorophores are present. Therefore, they are most appropriate for monitoring dynamic FRET. Methods E₄–E₆ provide FRET efficiency calculations with more complete cross talk correction. The principle is to remove the non-FRET contribution of the donor (donor emission observed in the band pass of the acceptor emission filter) and the contribution of the acceptor (emission of the acceptor when excited at the donor excitation wavelength) from the signal measured in the FRET channel in presence of both fluorophores. The underlying assumption is that the amount of cross talk is independent of the absolute intensity of the fluorophores and thus can be calibrated by ratiometric analysis of donor and acceptor signals. This permits the off-line calibration of cross talk ratios in samples containing only one of the two fluorophores at arbitrary concentrations. As with the methods E₂ and E₃, such precalibration allows the monitoring of FRET in dynamic systems. In contrast, Elangovan et al. (2003) propose a method (E₇) where the cross talk ratios are not considered constant but are determined at different fluorescence intensities. They generate an intensity-dependent look-up table, which is then used in the final calculation.

Method E₈ relies on the ratio of fluorescence intensity before and after acceptor photobleaching. The efficiency is calculated as the ratio of two intensities generated from two physically different samples (as for method E₁) or as the ratio of two intensities measured on the same sample but in two different regions (bleached and unbleached). The application of this method is often delicate in live biological samples due to long bleaching time and phototoxicity. Also, one has to ensure that the donor fluorescent properties are not impaired by photobleaching, and that the acceptor is completely bleached in appropriate time.

In summary, the essential difference between the methods reported in Table 1 consists in the observation strategy: In methods E₁ and E₈, the efficiency is measured by comparison of a situation with and a situation without acceptor. The actual transfer of energy is never observed directly, but the methods determine FRET indirectly. All other methods (E_2–7) rely on a direct measure of FRET that is taken upon the excitation of the donor and the observation of acceptor emission with subsequent correction of potential cross talk.

Six FRET indices are listed in Table 2, each using different cross talk corrections (see references for complete description). All of them involve as their basis the detection of an acceptor signal upon excitation of the donor.

As illustrated in these two tables, the proper use of FRET measurements to characterize molecular interactions requires corrections for 1), cross talk, 2), the fact that each of the measured fluorescence intensities consists of both FRET as well as non-FRET components, 3), the concentration of donor, and 4), the concentration of acceptor (Gordon et al., 1998). Item 1 gets particularly critical with dye pairs that constitute large spectral overlap and thus guarantee high FRET efficiencies. Hence, FRET microscopy suffers the paradox that the higher the signal, the more it is potentially deteriorated by systematic bias.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION FRET EFFICIENCY AND INDEX... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Our analysis of FRET efficiency is based on a well-defined coating of a coverslip with a solution containing a controlled amount of donor and acceptor.

Surface preparation
PLL-g-PEG-biotin (Huang et al., 2001; Kenausis et al., 2000) was adsorbed for 30 min on a glass coverslip (96-well with coverslip bottom imaging plates, BD Biosciences, Labware Europe, Le Pont De Claix, France) cleaned by oxygen plasma for 2 min. A solution containing streptavidin (Sa) labeled with donor (Sa-D) or acceptor (Sa-A) fluorophore or unlabeled (Sa-ul) was then adsorbed on the PLL-g-PEG-biotin for 30 min and rinsed three times with Hepes Z1.

The system was entirely controlled by the three following parameters (Fig. 1):

1. The ratio R_Biot = [PLL-g-PEG-Biotin]/[PLL-g-PEG-Total], which measures the amount of biotin competent for the adsorption of streptavidin. Optical wave-guide light-mode spectroscopy experiments showed that [Sa]_Surface, the amount of streptavidin on the surface, can be directly calculated from the ratio R_Biot via a linear relationship: [Sa]_Surface = 13.27 R_Biot [pmol/cm²] (Huang et al., 2001). In our experiments, R_Biot is 31%, and therefore [Sa]_Surface = 4.01 pmol/cm².
   
2. The ratio R_SA = [Sa-Labeled]/[Sa-Total]. By adding unlabeled streptavidin (Sa-ul) to the solution, we can control the mean distance between donors and acceptors.
   
3. The ratio R_DA = [Sa-D]/[Sa-A] describes the relative population of donors to acceptors in the solution. (e.g., in Fig. 1, R_Biot is 0.5, R_SA = 0.75, and R_DA = 1).
   

View larger version (16K): [in this window] [in a new window]   FIGURE 1  Surface FRET system on a coverslip coated with PLL-g-PEG-biotin. The biotin (black round) is tagged with streptavidin-donor (black star), streptavidin-acceptor (light gray star), and streptavidin-unlabeled.

Notation for distinguishing FRET channels and samples
The notation used in the article is the same as in Gordon et al. (1998), except for two minor modifications. The capital letter indicates the channel (D, A, or F, for donor, acceptor, or FRET channels) used to acquire the image (see Table 3 for microscope setup), and the small letter indicates the sample that was imaged (a, d or b, for samples with acceptor only, donor only, and both fluorophore classes). We introduce a notation with a double capital letter in italic to indicate, for a particular sample, the pixel-by-pixel mean ratio between two channels, e.g., DAa = mean(Da/Aa). The mean of the ratios is calculated over all unsaturated pixels in the two considered channels. In case of acceptor photobleaching, the term (ab) is added. (i.e., Db(ab) indicates the fluorescence measured in the donor channel when both fluorophores are present, but after acceptor photobleaching.)

Pinhole
Fully opened for wide field imaging.

Amplifier gain and offset
Initial investigations with unlabeled streptavidin surfaces showed that in all our experiments, the background level was only dependent on the amplifier settings, but not on the laser power and detection gain (data not shown). This supports that the molecular backbone of our model system does not contribute to the total signal by autofluorescence. Therefore, there was no need to apply any compensation of a background signal by electronic background correction. The amplifier offset was set to 0. On the other hand, we found that the amplifier gain also increased noise. To avoid any complication in reconstructing ratiometric data from different image acquisition channels, we consistently set the gain to 1 (no amplification).

Filter set
Described in Table 3.

Laser power and detector gain
A precalibration of the microscope revealed that detector gains are linear within a certain working range, and therefore each channel can be tuned separately for maximum signal. For each set of experiments (variation of R_DA or R_SA), we used the donor-only sample (d) with maximum R_DA and R_SA to set the gain in the donor channel (D), and determined the minimum laser power necessary to acquire a strong signal (Dd) at maximum detector gain. The same process was repeated for the acceptor channel (A) using an acceptor-only sample (a) with maximum R_SA but minimum R_DA. We set the parameters of the FRET channel (F) by keeping the same laser power as for channel D and by adjusting the detector gain so that the signal measured from the R_DA = 1, R_SA = 1 sample containing both fluorophores (b) yielded a value around the middle of the dynamic range.

Once set, these parameters were used throughout the entire experiment.

Background subtraction
To eliminate residual background signals that originated from uncompensated dark current of the photo-multiplier tubes, but not from sample autofluorescence (see above), we imaged PLL-g-PEG-biotin surfaces coated with unlabeled streptavidin in all channel combination and subsequently subtracted the mean value from all fluorescence signals.

FRET efficiency and FRET index
Several FRET efficiency and FRET indices have been calculated according to the methods described in Tables 1 and 2. Three types of surfaces were used: surface with acceptor only (a), surface with donor only (d), and surface with both donor and acceptor (b). For each of these surfaces, three quasisimultaneous images were taken in the three channels A, D, and F, (see Table 3), using the multi-tracking function of the microscope. This delivered nine images termed Aa, Da, Fa, Ad, Dd, Fd, Ab, Db and Fb, where Da and Fa, Dd and Fd, and Db and Fb were acquired exactly simultaneous using two separate photo-multiplier tubes. Calculations were made pixel by pixel and a map of FRET (efficiency or index) was reconstructed for each method. We excluded pixels from FRET calculations that were over- or undersaturated in any one of the three channels A, D, or F, for any of the samples a, d, or b. Since our surface was homogenously labeled, the mean efficiency or index over all remaining pixels provided a robust estimate of the amount of energy transfer for one experiment.

Monte Carlo simulation of FRET on surface
Simulations of energy transfer processes in 2D were performed using MATLAB (The MathWorks, Natick, MA, USA). The algorithm (see Appendix for a detailed explanation) implements a competitive scheme between multiple donors and acceptors, taking into account that already excited acceptors are not amenable to energy absorption. The competition between several donors potentially transferring energy to the same acceptor is resolved in a probabilistic sense, where the transfer probabilities depend on the geometry of donor and acceptor distribution. The simulation was controlled by the following parameters: [Sa]_Surface = 4.01 pmol·cm^-2; R_SA = [0.1..1]; R_DA = [10^-2..10²]; R₀ = [2..10] nm, T_int, and N_ex, where T_int is the integration time and N_ex is the number of excitons to be simulated. In our terminology, an exciton is a photon reaching a donor and, dependent on the donor's excitation state upon arrival, potentially participating in the process of donor excitation.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION FRET EFFICIENCY AND INDEX... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Results of the simulation
To generate reference FRET efficiencies for the experimental conditions of our surface system, we implemented a MCS package (see Appendix). In the following, we establish internal consistency of the MCS and generate predictions of experimental outcomes. All results presented are the mean of 10 runs performed for each of the tested parameter configurations (R_DA, R_SA, R₀) (for a definition of R_DA and R_SA, see Materials and Methods). Error bars in the graphs reflect the standard deviation of 10 repeated runs.

A system in two dimensions with multiple donors and multiple acceptors cannot be described by the single distance model
The single distance model describes the relationship between the distance r between one donor and one acceptor fluorophore and the transfer efficiency E (Lakowicz, 1999):

(1)

R₀ is the Förster distance, characteristic for the spectral overlap of the donor-acceptor pair (Lakowicz, 1999). In this model, it is assumed that one donor interacts with one acceptor. The model is applicable, for example, in the case where a donor and an acceptor dye molecule are coupled to two different domains of a molecule and variations in FRET efficiencies represent conformational changes (Suzuki et al., 1998; Mochizuki et al., 2001). However, for our situation where several donors and acceptors can interact, the single distance model cannot predict FRET efficiencies. Extensions of the model have been published by Wolber and Hudson (1979) and Dewey and Hammes (1980) for one donor with multiple acceptors. Yet, these more general models still do not describe the situation of multiple donors and multiple acceptors encountered with surface FRET. Here, an appropriate model should account for the following items:

1. Random distribution of donor and acceptor positions.
   
2. Random excitation of donors at random time points.
   
3. Already excited donors cannot be excited a second time. The energy is lost in the system.
   
4. Competition between excited donors to transfer energy to a nearby acceptor.
   
5. Saturation of the system when all acceptors around a donor are already excited and are not able to participate in the transfer process.
   

It seems difficult to find an analytical solution under all these conditions. However, the system can be elegantly simulated by an MC approach. The algorithm implements the events of fluorescence at the level of single fluorophores: A photon flux reaches the labeled surface. Whereas most of them are lost, those reaching a donor (and potentially participating in the process of its excitation) become "excitons". In the MCS, each excited donor can then either transfer its energy to an acceptor or emit fluorescence, according to the rules listed above. The simulated efficiency is simply calculated as the number ratio between transfer incidences and the number of used excitons.

MCS stability is flux dependent
The exciton flux is an important parameter for the stability of the MC predictions. Two issues define the stability of our MC FRET simulations:

How many excitons are necessary to guarantee robust statistics providing of FRET in a multi-donor, multi-acceptor system?

What is the maximum flux of exciton such that sufficient donors and acceptors are still excitable at any time point to participate in the competition between donor fluorescence emission and FRET (see Appendix)?

We have performed systematic tests (data not shown) to determine the two parameters defining the exciton flux: N_ex, the number of excitons, and T_int, the integration time over which these excitons are randomly released over the simulated sample. It turns out that N_ex = 10⁴ excitons guarantee robust statistics, and that for a flux of J = 10 excitons/ns, the donor-acceptor system remains sufficiently unsaturated to ensure a largely undistorted stochastic decision between donor fluorescence emission and FRET. Interestingly, the maximum exciton flux guaranteed experimentally (laser power = 25 mW, at 488 nm, with a 100x/1.4 objective, surface = 10⁴ nm², extinction coefficient = 78,000 M^-1·cm^-1, fluorophore concentration = 4.01 pmol/cm², R_DA = 1, R_SA = 1) is in the range of 15 excitons/ns, in good agreements with the MCS flux. This flux is dependent on the cross section area of the donor. Implicitly, the more donors, the greater the probability for a photon to become an exciton. Therefore, the exciton flux is proportional to the number of donors, i.e., proportional to the fraction of labeled molecules on the surface R_SA, multiplied with the fraction of labeled molecules being donors R_DA/(R_DA + 1), hence R_SA·R_DA/(R_DA + 1). To be consistent with the experimental setup, the MCS adapts the simulated exciton flux J_Sim to R_DA or R_SA as J_Sim = 2·J·(R_SA·R_DA/(R_DA + 1)).

The efficiency increases when the ratio donor/acceptor (R_DA) decreases
Fig. 2 A shows the dependence of MC simulated FRET efficiencies on R_DA. With low R_DA, the surface is almost entirely composed of acceptors. In this configuration, an excited donor has a higher probability to transfer its energy to a neighboring acceptor than to emit energy as fluorescence. The second effect of a high number of acceptors is that the probability that two donors compete for the same acceptor is almost zero. In combination, the two effects yield a high efficiency.

View larger version (23K): [in this window] [in a new window]   FIGURE 2  FRET efficiency dependence of fluorophore concentrations for different Förster distances. The exciton flux is set to 10 excitations/ns and the integration time to 1000 ns. (A) The fluorophore concentrations are modified via the donor-to-acceptor ratio (RDA) for a 100% labeling (RSA = 1). The dashed lines represent the value of the efficiency for different Förster distances calculated with the single distance model (Eq. 1), where r = Rc, the distance of closest approach (Rc = 5 nm). (B) The fluorophore concentrations are modified via the labeling ratio (RSA) with constant RDA = 1. The Förster distances R0 = 6.31 nm and R0 = 5.55 nm are those of the dye pairs Alexa 488-Alexa 546 and Alexa 488-Alexa 633, respectively. Data for R0 = 2 nm fall almost onto the abscissa of the graph, since Rc (=5 nm) is so much higher that the efficiency does not exceed 0.4%.

To perform an experiment investigating the effect of changes in the mean distance between donors and acceptors, a good choice for R_DA is in the range 1–20. In this range, the efficiency goes almost linear with the concentration ratio and the steep slope predicts high sensitivity in determining donor-acceptor distances from FRET measurements (see Fig. 2 A). For R_DA > 20, the efficiency goes to zero, and for R_DA < 1, the efficiency reaches a plateau where changes in R_DA have little effect on the efficiency. Both ranges preclude a quantification of molecular distances. Note that the R_DA range of the plateau depends on the Förster distance R₀ (discussed in more detail below). Therefore, in experiments that aim at the detection of small efficiency variations, it might be useful to carefully select the dye pair so that the working range of R_DA is in the linear domain.

The efficiency increases when the fraction of labeled molecules (R_SA) increases
Fig. 2 B indicates that a decrease of the fluorophore concentration reduces efficiency. In these simulations, R_DA is set to 1, and the concentration of both kinds of fluorophores is varied to modulate the mean distance between donor and acceptor. Since the probability of transfer is directly related to r⁶, we expect a strong dependence of the efficiency on R_SA, as is confirmed by the MCS.

The efficiency increases when the Förster distance R₀ increases
Six simulations have been run with different Förster distances R₀ (2, 4, 5.55, 6.31, 8, and 10 nm). Both graphs, Fig. 2, A and B, show that also in a multi-donor, multi-acceptor system, FRET efficiency is highly dependent on R₀.

In Fig. 2 A, efficiency values calculated with the single-distance model (dashed lines) and those simulated at low R_DA (R_DA < 0.1) (solid lines) yield comparable results for all R₀. In this configuration, there is no competition between donors for the same acceptor, leading to a situation where the main parameter influencing the probabilities of transfer is the Förster distance. Interestingly, our multi-donor, multi-acceptor simulation even predicts systematically higher efficiencies than the single-distance model. This underlines the fact that with several acceptors per donor, the cumulative probability for having transfer versus fluorescence is higher than the probability for a single transfer (cf. Appendix).

When R_DA increases (Fig. 2 A), the competition between donors for the same acceptor increases and the efficiency drops to zero. The same happens with a decrease of R_SA (Fig. 2 B). Here, the reduction in efficiency is related to the increase in distance between the fluorophores.

Experimental performance analysis
For each of the tested parameter sets (R_DA, R_SA, R₀), three surfaces were coated with either donor alone, acceptor alone, or both fluorophores according to the protocol described in Materials and Methods. Per experiment, five independent sets of images were taken in all channel and surface permutations at different positions on the sample, and FRET measures were calculated separately for each set according to the methods described in Tables 1 and 2. The values presented in the following sections represent the mean of the five sets.

FRET results depend on the method: a comparison of FRET efficiencies
We compare the methods E₁, E₄, E₆, E₇, and E₈ in Table 1. They include a ratio method using only one filter set and no correction for acceptor cross talk into the donor channel (E₁), three methods, which measure energy transfer directly with Fb and account for cross talk corrections with different schemes (E₄, E₆, E₇), and one method involving acceptor bleaching (E₈, discussed in a section below). Fig. 3 displays FRET efficiencies calculated with the five methods for changes in R_DA (A) and changes in R_SA (B). The data comprises two experiments using the dye pair Alexa 488-Alexa 546 (R₀ = 6.31 nm). All calculations rely on identical sets of input images, and the differences between the methods only relate to the differences in postprocessing. The methods can be examined in terms of 1), reproducibility between different experiments under identical conditions; 2), their ability to reflect changes in the parameters R_DA and R_SA consistently, and 3), their agreement with the MCS reference data (overlaid as black lines).

View larger version (23K): [in this window] [in a new window]   FIGURE 3  FRET efficiency calculated with five different methods for the dye pair Alexa 488-Alexa 546 (R0 = 6.31 nm). Surface coating parameters have been varied (RDA in A and RSA in B), and results of two experiments are shown as dotted and dashed lines. The black solid line represents the results of the MCS under the same conditions.

In contrast, the efficiency E₁, calculated from the signal ratio of the donor in presence and in absence of acceptor, does not provide repeatable results. In some cases, it even delivers negative efficiencies. Negative efficiency values indicate that the fluorescence of the donor in the presence of the acceptor is enhanced instead of quenched. In our particular case of an experiment with equal donor and acceptor concentrations (R_DA = 1), three out of five images showed higher intensity in Db than in Dd. This demonstrates the weakness of indirect measurements of FRET. The method is only stable with absolutely repeatable detection of the donor signal before and after adding acceptor and thus, notably, between two different samples. Small changes in the fluorescence, whether noise- or sample-induced, can dramatically alter the efficiency and yield nonsensical negative values. This behavior is confirmed by the graph in Fig. 3 B when the concentration of fluorophore decreases. Similar concerns apply to method E₈, although the weakness of this method will mainly be observable with the results in Figs. 4 and 8. Because of the method-inherent weakness of E₁, it is discarded from the rest of the experimental performance analysis.

View larger version (20K): [in this window] [in a new window]   FIGURE 4  FRET efficiency calculated with four different methods for the dye pair Alexa 488-Alexa 633 (R0 = 5.55 nm). Surface coating parameters have been varied (RDA in A and RSA in B), and results of three experiments are shown as dotted, dashed, and dash-dotted lines. The black solid line represents the results of the MCS under the same conditions.

View larger version (21K): [in this window] [in a new window]   FIGURE 8  Error of method E8 due to incomplete photobleaching relative to E6. The error is shown as a function of the fraction of bleached acceptor (solid line) and as a function of the fraction of bleaching cycles (dashed line).

The spectral overlap influences FRET sensitivity
Our surface FRET system offers the possibility to exchange the dye pairs (see Material and Methods) and thus to alter the Förster distance. Results from the same set of experiments as discussed before, but for the dye pair Alexa 488-Alexa 633 (R₀ = 5.55 nm), are presented in Fig. 4. This new pair tests a donor-acceptor system with on the one hand less spectral overlap and on the other hand higher spectral separation such that cross talk between channels is reduced. A low spectral overlap implies lower probabilities for FRET, and thus a decrease of signal-to-noise ratio (SNR). It also implies that the cross talk ratios are calculated between channels where the cross talk is close to zero. The correction factors become very sensitive to image noise, as illustrated in Fig. 4 A by the substantially weaker reproducibility of the experiments as compared to Fig. 3 A. Only data in the range 0.1 < R_DA < 10 is presented (see above). As in Fig. 3 B, the two methods E₄ and E₆ appear to generate more consistent and stable FRET values than E₇ (Fig. 4 B).

Our comparisons of FRET pairs with different R₀ lead to the following findings: The instabilities induced by the choice of a well-separated dye pair prevail over the advantages of low cross talk corrections. Actually, Fig. 3 suggests that cross talk can be well corrected, even for a dye pair with a large Förster distance.

Despite the lower reproducibility of the experiments with shorter Förster distance pairs, the data in Fig. 4 B, as compared to Fig. 3 B, are in better agreement with the MCS reference. The effect is less obvious with the comparison between Figs. 4 A and 3 A, although the data in Fig. 3 A exhibit also a trend for systematically lower experimental efficiency in the range R_DA = 0.1–1 relative to the MCS predictions. This suggests that the model and experiments suffer a disagreement, which is more severe for long Förster distances. In our model, the Förster distance is a function of the spectral overlap and the geometric factor, ², which takes into account the orientation of the donor dipole relative to the acceptor dipole (Lakowicz, 1999). The spectral overlap is characteristic for the spectral properties of the dye pair and is therefore a determined parameter. ², however is a free parameter that is dependent on the system. Dale et al. (1979) calculated the average ² to be in the case where the dyes are freely rotating. We used this value in our initial MCS shown in Figs. 2, 3, and 4. However, the existence of a mismatch between MCS and experiment motivated us to modify our MCS and to introduce a random ² for every donor-acceptor pair (see appendix, Eq. A2). The relative orientation of two dyes is calculated using three random angles, and the value of ² can range from 0 to 4. This leads to different R₀, and thus variable FRET probabilities for every donor-acceptor pair. Fig. 5 shows the results of the modified MCS (dashed line) in comparison to the uncorrected MCS (solid line). The calculations have been made for the same dye pair as in Fig. 3. Lower efficiencies are obtained from an MCS with random ² as compared to a fixed ² = , due to the fact that the distribution of random ² is skewed toward 0 (Fig. 5 B, inset), accompanied by a decrease of R₀.

View larger version (17K): [in this window] [in a new window]   FIGURE 5  Role of the orientation factor 2 in the simulated efficiency. The new simulated efficiency (dashed line) has been calculated with a random orientation factor. The mean of 10 runs is presented for an experiment where RDA varies (A) and where RSA varies (B). The solid line shows the simulated efficiency with 2 = and the dotted and dash-dotted lines depict experimental efficiencies calculated with method E6 as represented in Fig. 3. Inset, relative occurrence of all classes of 2 between 0 and 4.

FRET indices as qualitative measures of surface FRET
Fig. 6 shows the results obtained for four FRET indices. They have been calculated according to Table 2 for the dye pair Alexa 488-Alexa 546 (A) and for the dye pair Alexa 488-Alexa 633 (B). R_DA was varied from 0.01 to 100 for the first dye pair and from 0.05 to 20 for the second dye pair to have more data in the center of the curve. The inset in Fig. 6 A displays the results of the first dye pair for this range and allows immediate visual comparison with the graph in Fig. 6 B. In contrast to efficiency, different indices cannot be compared on an absolute scale. Therefore we have arbitrarily normalized all index values such that the index value equals 1 for R_DA = 1. Two behaviors can be distinguished in the results in Fig. 6 A: FRET₁ and FRET₃ are close to the simulated curve for R_DA > 1 and monotonically increase when R_DA decreases in good qualitative agreement with the MCS. Interestingly, whereas both MCS and FRET efficiency values exhibit a plateau, the indices seem to amplify its sensitivity in the range 0.01–1. FRET₆ and FRET₇ perform in a similar manner for R_DA > 1, but exhibit a turning point at R_DA = 1, which makes them essentially useless, at least for the range R_DA < 1.

View larger version (25K): [in this window] [in a new window]   FIGURE 6  Relative FRET indices calculated with four different methods for two dye pairs when RDA varies. Results of three experiments for the dye pair Alexa 488-Alexa 546 (panel A, R0 = 6.31 nm) and for the dye pair Alexa 488-Alexa 633 (panel B, R0 = 5.55 nm) are shown as dotted, dashed, and dash-dotted lines. The black solid line represents the results of the MCS under the same conditions.

Photobleaching of the acceptor is a method to vary the concentration of acceptors locally
We have tested our system with acceptor photobleaching for the dye pair Alexa 488-Alexa 546. Sixteen regions of interest (ROIs) were defined and photobleaching was performed in these ROIs with 1, 5, 10, 15, 20, 25, 50, 75, 100, 200, 300, 500, 750, 1000, 1500, and 2000 cycles, as shown in Fig. 7. The laser (1 mW He-Ne, 543 nm, maximum power) bleached the acceptor only, as verified with the control experiment illustrated in the inset of Fig. 7 A. The donor signal (blue) is retained, whereas the acceptor signal (green) decays in the expected way. Fig. 7 A represents the efficiency map calculated with method E₆. The results are color-coded and clearly display a decrease of FRET with photobleaching of the acceptor (increasing number of cycles from the upper left to the lower right.). The mean value of the efficiency calculated in the ROI is represented in Fig. 7 B as a blue solid line. After 2000 cycles, E₆ 0, suggesting that this is sufficient to completely bleach the acceptor.

View larger version (42K): [in this window] [in a new window]   FIGURE 7  Efficiency calculated for an experiment with progressive acceptor bleaching for the dye pair Alexa 488-Alexa 546. (A) False color map of FRET efficiency calculated with method E6 (see Table 1). The range goes from 0 (black) to 60% (yellowish green). The squares represent areas where the acceptor was bleached during 1, 5, 10, 15, 20, 25, 50, 75, 100, 200, 300, 500, 750, 1000, 1500, and 2000 cycles (from upper left to lower right). Inset, control experiment with bleaching of the donor alone (blue curve) and with bleaching of the acceptor alone (green curve). (B) FRET efficiency as a function of the bleaching cycle, calculated with method E6 (solid light blue line) and a fit of the curves (dotted light blue line). The relationship between the number of bleach cycles and the mean distance for energy transfer (see text) is illustrated with the black solid line. Inset, relationship between the number of bleaching cycles and RDA (calculated based on the fit curve in B and the interpolated E6 efficiency as a function of RDA taken from Fig. 3 A).

Incomplete photobleaching induces errors in the calculated efficiency
Acceptor photobleaching is also a frequently used approach to measure FRET, as discussed in Table 1. The corresponding efficiency is given by E₈ = 1 - Db/Db(ab), relying on the ratio of donor signal before and after complete bleaching of the acceptor. In our case of a homogeneously labeled surface, we chose a slightly different observation strategy. Only a part of the surface was bleached. Thus, the same image showed a region where both fluorophores were still present, providing a measure for Db, and an acceptor-bleached region, providing a measure for Db(ab). This protocol bears the advantage of circumventing problems of sequential observation, e.g., arising from global intensity changes due to focus drift between the acquisition of Db and Db(ab). In a less-controlled sample with inhomogeneous labeling, similar stability can be attained with sequential observation when a control region is coimaged, delivering two donor intensities, Db^c and Db^c(ab) that are unaffected by the acceptor bleaching. The modified method is insensitive to global variation of the intensity and may have the same characteristics as E₈ applied to our idealized model sample.

We have investigated the performance of this method in reporting FRET efficiency as a function of R_DA, R_SA, and R₀. Results are shown in Figs. 3 and 4. The reference value Db(ab) was taken after 2000 bleaching cycles, according to our findings in Fig. 7 B.

The results essentially agree with those obtained with the other methods, although in general the values seem to be lower. When R₀ decreases (Fig. 4), they exhibit large fluctuations, implying increased sensitivity to noise.

The method bears the advantage of using a single sample and a single filter set but strictly relies on complete photobleaching of the acceptor. In practice, such an approach is often problematic: First, to guarantee proper bleaching, one has to tune the laser power, bleaching wavelength, and bleaching time. Second, bleaching can have cross talk and thus affect the donor signal as well. Third, in live cell imaging, bleaching is known to cause phototoxicity and thus to severely affect the sample viability. It is therefore important to choose an acceptor that can be readily bleached. Our choice of Alexa 546 would obviously be not optimal for life experiments, since Alexa dyes are known to be very stable (as confirmed by the large number of cycles necessary for complete bleaching).

More critical for our performance analysis, however, are errors induced by incomplete bleaching. The method E₈ strictly relies on the assumption that the acceptor is entirely bleached. In the practice of, e.g., a live cell experiment, this can frequently not be guaranteed, as acceptor molecules are subjected to diffusion and other protein dynamic processes, and the assessment of the number of cycles necessary for complete bleaching is not straightforward. Fig. 8 shows the relative error estimated under incomplete acceptor photobleaching in comparison to method E₆. The results are presented as a function of the fraction of acceptor bleached (solid line) and as a function of the number of bleaching cycles (dashed line). If only 70% of the acceptors are bleached, the error in FRET efficiency is 50%. Even worse, the gradient in the error curve increases between 70% and 100% bleaching, which means that there is no tolerance at all for incomplete bleaching. Fig. 8 shows that despite a 100% photobleaching, the method E₈ still provides a 10% error. This error is mainly due to difference in the observation strategy and uncorrected cross talk.

Uncertainty analysis of different FRET methods
Incompatibilities between the different FRET methods can be due to two factors:

1. Differences in observation strategy and cross talk correction.
   
2. Differences in the robustness against uncontrolled changes (irreproducibility) in the intensity measurement of any channel and against noise.
   

Observation strategies relying on a physical exchange of samples are inferior to those recovering FRET from ratio and difference analysis of samples coimaged in different channels
Depending on the observation strategy, the methods described in Table 1 can be classified into two groups:

1. Methods E₁ and E₈ calculate the efficiency from the change of donor fluorescence in images taken from different samples (Db with and Dd or Db(ab) without acceptor). Fig. 3 shows that the efficiencies calculated with these methods can be negative. This problem is inherent to the chosen observation strategy. Any change in the absolute fluorescence intensity between the acquisition of the two images directly affects the FRET efficiency. Such changes are very likely. With method E₁, it is almost impossible to ensure twice the same donor distribution in an experiment, one in absence and one in presence of acceptor. With method E₈, mainly the bleed-through of the laser line used for acceptor bleaching and mobility of the donor bear the risk of altering the donor fluorescence in an uncontrolled manner. For the same reason, both methods are weak in analyzing FRET in dynamic systems.
   
2. In contrast, all other methods derive the efficiency from the signal obtained in the FRET channel in the presence of both fluorophores (Fb). They only differ in the applied cross talk correction factors, but none of them involves an exchange of the sample. To illustrate this, we examine, for example, method E₄. It relies on the measure of Fb, from which the cross talk in Db and Ab is subtracted. All three measures are taken from the same sample (b) coimaged in three different channels. The cross talk factors (FDd and AFd for sample d and FAa for sample a) are again calculated from signals comeasured on the same sample (either d or a). Importantly, the equations do not contain any ratio or subtraction that combines the signals of two different samples. Therefore, the only uncertainty of these ratio or subtraction terms arises from dynamic changes of one sample between the observation in two different channels. For many applications and microscope setups, including the one employed for this paper, sample variation during the switch of channels are negligible.
   

To illustrate the sensitivity of method E₁ to changes in the absolute level of fluorescence, we present in Table 4 A an example of intensities obtained for an experiment with R_DA = 1 and R_SA = 1 yielding negative E₁. In this particular case, Db is larger than Dd, most probably because of an uncontrolled increase of donor concentration between the sample d and b. In practice, it is often difficult to guarantee the same range of absolute donor fluorescence for two different samples. In our case, irreproducibilities can occur with different levels of donor protein adsorption and focus shifts. In live cell experiments, the problem gets even more prominent. Different cells will hardly ever express the same amount of protein, and changes in the experimental conditions, e.g., in temperature or pH, can have dramatic effects on the signal. We have measured the sample irreproducibility by taking five independent images per experiment. For the sample b, we found a standard deviation of 16%–38% of the channel mean intensity, indicating that even in our highly controlled surface FRET system, the fluorescence signal is subject to significant variation. These experimental difficulties affect methods E₂–E₇ much less for the reasons illustrated in the next two sections.

Influence factors indicate the effect of uncontrolled signal changes
To analyze the effect of uncontrolled signal changes, we have calculated for each of the methods the influence factor of every channel. The influence factor _i of a channel i denotes the change in FRET efficiency induced by a change in the intensity of this channel. In addition, we introduce the relative influence factor, _i, as a measure of the relative change in efficiency induced by a relative change in the intensity of channel i. _i and _i are calculated according to:

(2a)

(2b)

where is the nominal efficiency for a certain donor and acceptor configuration and I_i denotes the intensity of the ith channel, i = 1..9. In our case, is estimated by MCS. The relative influence factors _i are listed in Table 4 B for methods E₁, E₄, E₆, and E₇ considering an experiment with R_DA = 1 and R_SA = 1.

For all methods except E₇, relative influence factors greater than 1 are obtained for at least one channel. This means that uncontrolled relative changes in the signal propagate adversely, amplifying the relative error of the FRET efficiency, as well. However, there is only a small difference in the magnitude of the relative influence factors between the method E₁, which we found unstable in presence of signal irreproducibility, and the clearly more stable methods E₄ and E₆. The maximum |_i| of method E₁ is 2.1 in both Dd and Db, whereas E₄ and E₆ both have a maximum |_i| in Fb of 1.7 and 1.5, respectively. Obviously, the instability in E₁ must be associated with the fact that irreproducibilities in Dd and Db propagate independent and uncompensated, whereas the channel contributions of E₄ and E₆ grant a compensation of irreproducibilities in Fb by other terms.

Methods with ratio and subtraction terms combining the signals of the same sample have compensating relative influence factors and thus are robust against image irreproducibility
It turns out that the fundamental difference between E₁ and the more robust methods E₄, E₆, and E₇ consists in the absence versus existence of cross-compensating influence factors. For example, an increase by x% of Db due to an uncontrolled increase in donor concentration of sample b relative to sample d yields a decrease of -2.1·x% in E₁. In contrast, the same increase yields a decrease of -1.5·x% in E₄, but at the same time, the signals Ab and Fb will increase, nearly canceling the effect of one another. Thus, uncontrolled variation of the sample has little effect on E₄ as long as the channels Ab, Db, and Fb are imaged under identical conditions. A similar cross-compensation of relative influence factors is found for the two other samples a and d in all methods listed in Table 4 B except E₁. Cross-compensation is indicated by bold numbers grouping the factors of the three channels A, D, and F for each sample a, d, and b. In each of the groups, e.g. {Aa, Da, Fa} the sum of the factors is almost zero, explaining the robustness of E₄, E₆, and E₇ against uncontrolled changes between the samples. The same is true for the groups {Ad, Dd, Fd} and {Ab, Db, Fb}.

The influence of image noise precludes robust analysis in extreme R_DA and R_SA
Fig. 9, A–D, illustrate the relative influence factors in the range 0.01 < R_DA < 100, R_SA = 1 for methods E₁, E₄, E₆, and E₇. Three domains can be observed in all panels:

View larger version (34K): [in this window] [in a new window]   FIGURE 9  Relative influence factors as a function of RDA for methods E1 (A), E4 (B), E6 (C), and E7 (D).

Domain 2. The influence factors are low (smaller than 5). This indicates that the efficiency calculated in this domain is much less susceptible to noise than in domain 1. Indeed, the data in block R_DA =1 in Table 4 C suggest an overall uncertainty of E₆ of 0.12, resulting in a confidence interval (E₆ = 0.6 ± 0.12, 20% relative uncertainty). This finding is supported by the small variation of FRET efficiencies in this domain in Fig. 3.

Domain 3. The influence factors increase dramatically when R_DA increases (e.g., Fig. 9 C, E₆). This renders the calculation of FRET efficiency instable. Comparable to domain 1, the uncertainty amounts to ±0.59, but owing to inherently low efficiencies in this domain, the relative uncertainty reaches now a level of up to 4000%.

We conclude from this analysis that the cumulated effect of noise propagation of each channel can predict the variation of FRET, calculated with E₆, including the nonsensical negative values for extreme R_DA found in Fig. 3. Similar conclusions can be drawn for the methods E₄ and E₇ (data not shown), whereas the instabilities of E₁ and E₈ originate in the unfavorable propagation of uncontrolled changes in donor concentration between the samples d and b, and focus shifts (see above).

	CONCLUSION

TOP ABSTRACT INTRODUCTION FRET EFFICIENCY AND INDEX... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
There were a number of reasons to undertake the analysis presented in this paper. At the beginning of implementing a FRET assay, it is surprising to see that the literature abounds with methods to measure FRET. They deliver a zoo of numbers, factors, indices, and values, which are difficult to compare. Our first goal was to sort the methods and to rewrite them in a consistent terminology inspired by the one suggested by Gordon et al. (1998). This allowed us to distinguish between methods reporting absolute measures of FRET (FRET efficiencies, Table 1) and those reporting relative measures (FRET indices, Table 2), and to classify them in terms of the data and equipment requirements (filter set per number of samples per number of images). Second, we evaluated their performance using a surface FRET system that could be controlled in terms of absolute and relative fluorophore concentrations, i.e., in terms of sensitivity and mean donor-acceptor distances. In addition, the system could be modeled computationally, providing a reference value for a performance test on an absolute scale.

We have found that FRET efficiencies can only be extracted for R_DA in the range 0.1–10. In this range, E₆ (Gordon et al., 1998) appears to be the most accurate. For R_DA < 0.1, FRET can still be evaluated, although, only qualitatively, with FRET indices (FRET₁ or FRET₃), which turn out to increase the sensitivity in a low donor regime. For R_DA > 10, the number of acceptors is insufficient for a reliable transfer measurement. The exact breakdown depends on the signal-to-noise characteristics.

Comparisons of our results with the predictions made by Kenworthy and Edidin (1998) confirm that in our system, the fluorophores are randomly distributed on the surface and do not cluster: E is dependent on acceptor surface density and E goes to zero at low surface densities.

Our system also allowed an evaluation of one of the most frequently used methods of FRET quantification: acceptor photobleaching. The results obtained with this method are in good agreement with those of other methods, if the photobleaching is complete. The error due to incomplete photobleaching, however, can go up to 100%, and is still 50% if the acceptor is bleached to only 30% of its initial intensity. Incomplete photobleaching will almost always be the reality of a live cell experiment if the acceptor dye is not carefully chosen. We will therefore discard this method for our upcoming measurement in live yeast.

In summary, our main findings with a controlled FRET system, supported by MCS predictions, are the following:

Donor and acceptor concentration should be of the same order of magnitude, and stable FRET measurements can only be achieved in the range of donor-to-acceptor ratios 0.1–10. Outside this range, noise and data irreproducibility propagate unfavorably, rendering accurate efficiency calculations impossible.

The various FRET methods reported in the literature vary greatly in terms of the reported efficiency or indices, and not all of them seem stable inside the range of donor-to-acceptor ratios 0.1–10.

To get stable FRET measurements, the transfer has to be observed in the FRET channel, i.e., by excitation of the donor and a measurement of the acceptor emission. Methods that estimate FRET from the donor signal variation in presence and absence of acceptor (E₁ or E₈) are less robust.

To get stable FRET measurements, the dye pair with the maximum spectral overlap should be used.

This, however, requires cross talk correction as such dye pairs tend to be accompanied by substantial cross talk in the imaging channels. As written by Gordon and colleagues, there is no need to reject a donor and acceptor combination on the basis that a donor signal can be detected in the acceptor channel. All methods proposing cross talk corrections yield results that are close to the results obtained with the simulation.

Some FRET indices report FRET very reproducibly and still allow qualitative measurements of FRET in cases of donor-to-acceptor ratios <0.1 where efficiency measures fail or are completely insensitive toward distance variations.

	APPENDIX

TOP ABSTRACT INTRODUCTION FRET EFFICIENCY AND INDEX... MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
MONTE CARLO SIMULATION ALGORITHM
The simulation involves the following steps (Fig. 10):

1. The number of excitons N_ex is set as a function of R_DA and R_SA.
   
2. A surface is generated and donor and acceptor are placed randomly on the surface according to the parameters [Sa]_Surface, R_SA, and R_DA. In Fig. 10, a gray box indicates the use of the random generator. We take into account that the molecules carrying the fluorophores have a certain size, which defines an exclusion radius R_c (5 nm for streptavidin).
   
3. The program generates for every donor a list of acceptors in a circular region of radius 10 R₀. For distances >10 R₀, the probability for t