TripleFRET measurements in flow cytometry


  • Ákos Fábián,

    1. Department of Biophysics and Cell Biology, Research Center for Molecular Medicine, Medical and Health Science Center, University of Debrecen, Hungary
    Search for more papers by this author
    • Á. Fábián and G. Horváth authors contributed equally to the article.

  • Gábor Horváth,

    1. Institute of Innate Immunity, University Hospitals, University of Bonn, Germany
    Search for more papers by this author
    • Á. Fábián and G. Horváth authors contributed equally to the article.

  • György Vámosi,

    1. Department of Biophysics and Cell Biology, Research Center for Molecular Medicine, Medical and Health Science Center, University of Debrecen, Hungary
    Search for more papers by this author
  • György Vereb,

    1. Department of Biophysics and Cell Biology, Research Center for Molecular Medicine, Medical and Health Science Center, University of Debrecen, Hungary
    2. MTA-DE Cell Biology and Signaling Research Group, Research Center for Molecular Medicine, Medical and Health Science Center, University of Debrecen, Hungary
    Search for more papers by this author
  • János Szöllősi

    Corresponding author
    1. Department of Biophysics and Cell Biology, Research Center for Molecular Medicine, Medical and Health Science Center, University of Debrecen, Hungary
    2. MTA-DE Cell Biology and Signaling Research Group, Research Center for Molecular Medicine, Medical and Health Science Center, University of Debrecen, Hungary
    • Department of Biophysics and Cell Biology, Faculty of Medicine, Medical and Health Science Center, University of Debrecen, P.O.Box 39, Nagyerdei krt. 98, H-4012 Debrecen, Hungary
    Search for more papers by this author


This article is corrected by:

  1. Errata: TripleFRET measurements in flow cytometry Volume 83A, Issue 7, 672, Article first published online: 21 May 2013


A frequently used method for viewing protein interactions and conformation, Förster (fluorescence) resonance energy transfer (FRET), has traditionally been restricted to two fluorophores. Lately, several methods have been introduced to expand FRET methods to three species. We present a method that allows the determination of FRET efficiency in three-dye systems on a flow cytometer. TripleFRET accurately reproduces energy transfer efficiency values measured in two-dye systems, and it can indicate the presence of trimeric complexes, which is not possible with conventional FRET methods. We also discuss the interpretation of energy transfer values obtained with tripleFRET in relation to spatial distribution of labeled molecules, specifically addressing the limitations of using total energy transfer to determine molecular distance. © 2013 International Society for Advancement of Cytometry

Fluorescence Resonance Energy Transfer (FRET), originally described by T. Förster (1), is a nonradiative energy transfer process taking place between an excited donor fluorophore and an acceptor dye. The rate of energy transfer is inversely proportional to the sixth power of the separation between the donor and the acceptor. In the past several decades, this phenomenon was implemented in biological systems as a nanometer-scale ruler to view molecular distances and association patterns (2–8). To date, a myriad of methodologies have been developed to measure FRET efficiency, although most of these were limited to examining the interaction of only two different proteins at a time (9–13).

The realization that a multitude of processes in cellular biology are not restricted to the interaction of only two molecules has fueled efforts to expand traditional two-dye FRET measurements to include more interaction partners. Recently, several articles investigated the possibility of measuring FRET between three distinct fluorescent molecules (14–26). The major aims of these studies were to establish the theoretical background for tripleFRET measurements and use the method in biologically relevant experiments. The multiple FRET processes that can occur between three fluorophores were thoroughly characterized by Watrob et al. (16) by using DNA-bound dyes with known distances. An interesting observation was that the presence of an intermediate fluorophore sensitizes the FRET process and extends the detectable distance range by about 50%. The three-color FRET phenomenon was also used to study single-molecule Holliday-junction dynamics with donor photobleaching experiments by microscopy (22). Another study showed the applicability of fluorescent proteins (CFP, YFP, and mRFP) to three-fluorophore FRET in live cell imaging (20). The approach was validated with cleavable protein-linked fluorescent proteins, and afterwards the interaction of stimulated EGFR with adaptor proteins (Grb2 and Cbl) present in signal transduction was analyzed using acceptor photobleaching and intensity-based microscopic techniques. A similar approach was used for the determination of TRAF2 homotrimerization in flow cytometry (27). In a more recent study, three-chromophore FRET was used to reliably discriminate between DNA strands labeled with the same three fluorescent dyes but with different intrastrand dye distances (23).

Although these studies described the phenomenon properly and demonstrated their applicability to biological samples, they had restrictions concerning specimen selection (for instance using rigid DNA strands) (15, 22–25, 28) or simplifications in the analysis (neglecting possible transfer processes, thus obtaining only semi-quantitative FRET values) (22, 27). Simplifications were made because three-dye systems are exceedingly more complex than conventional two-dye systems, with spectral bleed-through from multiple fluorophores often obscuring the true FRET signal. Several workarounds were developed, either simplifying the imaging of three molecules to two fluorophores (29) or forgoing complications arising from simultaneous imaging of dyes with sequential bleaching (30). However, these methods either require extensive molecular biology work to prepare adequate samples, or the imaging process is itself cumbersome and does not allow for live-cell or high-throughput imaging. A general, relatively easy-to-implement method applicable to biological systems with variable molecular stoichiometries (such as cell surface protein clusters) has not been presented.

In this study, we discuss mathematical algorithms to calculate FRET efficiencies for three-dye systems on a cell-by-cell basis for flow cytometry. The method does not require any special instrumentation beyond a commercial flow cytometer capable of excitation at three distinct wavelengths and acquisition of six intensity channels. Preparation of samples is fast, as labeling with fluorescently tagged antibodies is sufficient for the measurement. Furthermore, the FRET calculation does not require separate measurement of unquenched donor intensities, thereby minimizing artifacts introduced by inter-sample (and cell-by-cell) variability.

Materials and Methods

Cell Lines

Human gastric cell line N87 with high ErbB2 and major histocompatibility complex class I expression level (31) was obtained from the American Type Culture Collection (Rockville, MD) and grown according to the manufacturer's specification (in RPMI containing 10% fetal bovine serum, 2 mM L-glutamine, and 0.25% gentamicin in 5% CO2 atmosphere) to confluency. For flow cytometry, cells were harvested by treatment with 0.05% trypsin and 0.02% ethylenediaminetetraacetic acid before antibody labeling.

Conjugation of Antibodies with Fluorescent Dyes

In our experiments, we used the following anti-erbB2 antibodies: pertuzumab (a gift from Hoffman-La Roche, Grenzach-Wyhlen, Germany); trastuzumab (purchased from Hoffman-La Roche, Grenzach-Wyhlen, Germany); and H76.5 antibody (prepared from the hybridoma cell line, a kind gift of Yosef Yarden). Aliquots of antibodies (about 1 mg/ml concentration) were conjugated with the succinimidyl ester derivative of Alexa Fluor 488 (dye A), Alexa Fluor 546 (dye B), or Alexa Fluor 647 (dye C), Life Technologies, Carlsbad, CA, dyes according to the manufacturer's specifications. The labeling ratios were in the range of2–4, where concentration quenching does not have a significant effect on the fluorescence quantum yield of the fluorophores (32). Relevant excitation and emission spectra of these fluorescent dyes are shown in Figure 1.

Figure 1.

Normalized excitation and emission spectra of donor and acceptor fluorophores. The gray shaded area corresponds to the overlap integral of the emission spectrum of dye A and excitation spectrum of dye C.

Labeling Cells with Fluorescent Antibodies

For flow cytometry, freshly harvested cells were washed twice in ice-cold phosphate buffered saline (PBS; pH 7.4). The cell pellet was suspended in PBS at a concentration of 2 × 107 cells/ml. Then 25 µl of conjugated antibodies were added to 25 µl of cell suspension and cells were incubated for 30 min on ice. The excess of antibody was at least fivefold above saturating concentrations during incubation. The same procedure was used for FRET samples, in which a mixture of donor- and acceptor-labeled antibodies was added to the cell suspension. Labeled cells were washed twice with cold PBS and fixed with 1% formaldehyde in PBS.

Instrumentation and Sample Measurement

For flow cytometric measurements, we used a FACSVantage SE with DiVa option flow cytometer (Becton Dickinson, Franklin Lakes, NJ) equipped with a 488-nm water-cooled Argon-ion laser, a 532-nm diode pumped solid-state laser and a 633-nm air-cooled HeNe laser. The fluorescence detection channels (emission filters and laser wavelengths used for excitation) for the three fluorophores are shown in Table 1.

Table 1. Laser excitation wavelengths and emission filters of intensity channels
ChannelLaser wavelength (nm)Filter
I5532650 LP
I6633650 LP

Theory of FRET

FRET is a nonradiative energy transfer process, in which an excited donor molecule excites an adequately oriented fluorescent acceptor molecule via a long distance dipole-dipole interaction. Transfer efficiency, which is the probability that a donor excitation quantum is transferred to an acceptor, is given as:

equation image(1)

where ktransfer is the rate constant of energy transfer and kother is the sum of the rate constants of all other de-excitation pathways. The distance dependence of the transfer efficiency is described by the following equation:

equation image(2)

where r is the separation of the donor and acceptor and R0 is the so called Förster distance characteristic for the donor-acceptor pair. The Förster distance is defined as the distance at which the transfer efficiency between donor and acceptor is 50%. This distance dependence makes FRET efficiency a sensitive indicator of intermolecular distance.

The presence of FRET results in the quenching of donor intensity and a simultaneous increase in acceptor fluorescence. Multiple methods of FRET calculation exist, some of which are based on the measurement of fluorescence lifetime, whereas others use quenching of the donor or sensitized emission of the acceptor (9).

Theory of TripleFRET

Although a three-fluorophore FRET system is seemingly complicated, it can be easily described by two distinct schemes as shown by Watrob et al. (16). If we denote the fluorophores with increasing excitation wavelength (e.g., blue, green, and red) as A, B, and C, these schemes are as follows (see also Fig. 2.): (1) the so-called relay or two-step FRET process, when the energy from donor A is channeled to C via B, and (2) two competitive FRET processes from donor A to acceptor B and from donor A to acceptor C. Naturally, there is also a third scheme, which is a combination of the previous two when all possible FRET processes are allowed.

Figure 2.

Schematic drawing of a three-dye system with possible energy transfer routes. EAB and EAC values refer to transfer efficiencies measured in the presence of competition between transfer processes from A to B and A to C. Erelay = EABEBC is the transfer efficiency between A and C via B, Etotal = EAC + Erelay is the total probability of energy transfer from A to C via the direct and indirect mechanisms.

In the first case, the relay FRET efficiency (Erelay) can be given by the product of the two individual FRET efficiencies:

equation image(3)

For the second case, since the two FRET processes are competing for the same donor A, their individual FRET efficiencies (EAB and EAC) have to be corrected for this competition. Fortunately, these competitive FRET efficiencies (EAB and EAC) can be calculated from the noncompetitive two-dye FRET efficiencies:

equation image(4)
equation image(5)
equation image(6)

In the third case, both relay and competitive FRET can occur, and total FRET efficiency (Etotal) is the sum of relay and direct FRET corrected for competition for donor A:

equation image(7)

Evaluation of Transfer Efficiency

All transfer efficiencies were calculated with the equation set described in the Results section of this article, unless otherwise indicated. To evaluate FRET data obtained with flow cytometry, a much-improved version of the AFlex software, ReFlex (free-ware, available at was used with the equations entered in the equation editor of the program and applying manual gating (33) (for the gating strategy please see the Supporting Information). Transfer efficiency values are given as median values of transfer efficiency histograms. Flow cytometric dotplots and histograms were generated with ReFlex, three-dimensional transfer efficiency scatter plots were created with Wolfram Mathematica 7 (Wolfram Research, Champaign, IL).

Determining Cross-Excitation, Spillover, and Alpha-Factors

Each fluorophore used has its “native” detection channel corresponding to its optimal excitation and detection wavelengths. In most channels, however, the emissions of two or all three dyes are mixed. Cross-excitation and spillover factors (S1S12) account for the emission of dyes in channels not native for the given dye. S factors were measured on single-labeled samples according to Eqs. (10)–(12). Samples labeled with Alexa Fluor 488 were used to calculate S1 and S9; samples labeled with Alexa Fluor 546 to calculate S2, S4, S10, and S12; and samples labeled with Alexa Fluor 647 to calculate S3, S5, and S7.

Alpha factors are scaling factors correcting for the difference in the fluorescence quantum yields and detection efficiencies of donor and acceptor fluorophores. The alpha factor can be considered as a “currency exchange rate” to scale loss of donor emission to gain of acceptor emission. To calculate the alpha factor, the intensity of the same number of excited donor and acceptor fluorophores has to be measured at given wavelengths. This is most easily done by labeling a cell-surface protein with donor- and acceptor-tagged antibodies in separate samples. Alternatively, two different antibodies can be used that do not compete with each other for binding and that recognize epitopes far enough apart so that energy transfer does not occur (34, 35). Another possibility is to apply epitopes with known distances and well characterized transfer efficiencies, and set the value of alpha to yield the reference transfer efficiencies (34). When using fluorescent proteins, donor-acceptor fusion proteins can be constructed where the expression level of both fluorophores are the same. By varying the length of the linker region (36) or by using an iterative method yielding E and alpha simultaneously (37), alpha can be calculated.

For our experiments, the average intensity of several thousand cells singularly labeled with Alexa Fluor 488, Alexa Fluor 546, or Alexa Fluor 647 was used to obtain average intensities for the calculation of alpha factors. The effects of errors of S and alpha factors on measured transfer efficiency are shown in Section 6 of the Supporting Information.


TripleFRET Measurements in Flow Cytometry

To measure FRET efficiency on a cell-by-cell basis, both donor quenching and sensitized emission had to be considered and a corresponding set of equations has to be solved. Below, we present an initial set of equations for the scenario, where both relay and direct energy transfer from A to C take place (equations and their solutions for the cases of relay transfer only, direct transfer only and no direct or relay transfer can be found in the Supporting Information section). Six independent emission intensities I1I6 can be identified and broken down into terms due to direct excitation and sensitized emission of the dyes: I1: quenching of donor A (by acceptors B and C), native intensity channel to detect dye A; I2: sensitized emission (from donor A) and quenching of acceptor B (by acceptor C), I3: sensitized emission of acceptor C (from donor A and donor B excited through donor A), I4: quenching of donor B (by acceptor C), native intensity channel to detect dye B; I5: sensitized emission of acceptor C (from donor B); and I6: native intensity channel to detect dye C.

equation image(8)

As we wanted to give a full representation of the system, equations include the competitive FRET efficiencies EAB and EAC for FRET from A to B and from A to C, respectively. There are altogether seven unknowns: three unperturbed intensities IA, IB, and IC from the three dyes (that would be measured in the absence of FRET) and four transfer efficiencies EAB, EAC, EBC, and Erelay. Since in its present form the equation system is underdetermined (with only six independent equations for seven variables), a further equation is required for a solution. Therefore Eq. 3 is used (in a slightly modified form to account for competition between dyes B and C) for a seventh independent equation:

equation image(9)

The spillover and cross-excitation factors (S1S12) were calculated from single-labeled samples in the following way (where Iq p is the intensity in channel p of a sample labeled with only dye q conjugated to antibodies):

equation image(10)
equation image(11)
equation image(12)

The alpha-factors can be determined empirically by the following formulas (where L X is the labeling ratio of the antibody with fluorophore X and ε X is the molar extinction coefficient of fluorophore X at the indicated wavelengths):

equation image(13)

Upon substituting Eqs. (9)–(13), the equation set 8 gives very complicated solutions for all unknowns (except for IC). In our experiments S5 was reproducibly 0 and therefore it was omitted from calculations thereby simplifying the formulas (however, it was measured each time to verify the validity of such a simplification). The solutions contain several terms, which upon factorization make the equations look simpler and their physical meaning more prominent. These terms are labeled as I X 1I X 5, and can be considered as donor quenching (I X 1 and I X 4) and bleed-through corrected sensitized emission (I X 2, I X 3, and I X 5) intensities:

equation image(14)

Using the equations above, we arrive at the following solutions for the equation set (8):

equation image(15)
equation image(16)
equation image(17)
equation image(18)

The noncompetitive FRET efficiencies can also be calculated using Eq. (6):

equation image(19)
equation image(20)

Based on Eq. (3), Erelay can also be given with the factorized terms:

equation image(21)

After substituting into Eq. (7), Etotal (the total percentage of the energy absorbed by dye A that is eventually passed on to dye C) can be calculated as:

equation image(22)

Or in a more simplified form:

equation image(23)

Transfer Efficiencies of Two- and Three-Dye Systems

To test our calculation method, first N87 cells were labeled with different antibodies against the ErbB2 protein. Samples were prepared as a three-dye system as well as a corresponding set of two-dye systems (Table 2). For validation purposes and to demonstrate the applicability of our method in three-dye systems, all samples were evaluated (in addition to our own equations) using an intensity-based method previously developed and tested for two-dye systems (38; for a detailed description of the equations used for FRET analysis, please see the Supporting Information). The use of non competing antibodies against different epitopes of the same protein ensured intramolecular binding and proximity of the dyes (4, 39). The results of these measurements are listed in Table 2. All permutations of a two-dye system with the three fluorophores resulted in measurable transfer efficiencies. Analyzing FRET in two-dye systems according to the tripleFRET method produced identical transfer efficiency values as conventional two-dye intensity-based FRET analysis. FRET analysis of the three-dye system with tripleFRET resulted in transfer efficiency values very similar to the ones obtained in two-dye systems. Correction for competition between the two acceptors further increased the agreement with the values from two-dye systems. At the same time, traditional intensity-based FRET failed to reproduce the FRET values of the two-dye systems in the triple-labeled sample. Specifically, EAB was underestimated (7.9% instead of 13.4%) and EAC overestimated (11.4% instead of 4.9%). The addition of dye B to the labeling scheme consisting of only dyes A and C substantially increased the total energy transferred from A to C, providing evidence for a relay transfer process in our intramolecular model system.

Table 2. Measured transfer efficiencies (%) in various dye systems
Labeling schemeDye A: Alexa Fluor 488Dye B: Alexa Fluor 546Dye C: Alexa Fluor 647
Double (AB)H76.5Trastuzumab
Double (AC)H76.5Pertuzumab
Double (BC)TrastuzumabPertuzumab
 Double (AB)TripleDouble (AC)TripleDouble (BC)Triple
E as two-dye13.57.94.911.445.144.3
  1. Measured EAB, EAC, and EBC median transfer efficiencies in three-dye and corresponding two-dye systems. E as two-dye: traditional intensity-based FRET analysis used for two-dye systems (38); E′, E, Erelay, and Etotal are competitive, noncompetitive, relay, and total FRET efficiencies calculated with the tripleFRET method; N.A.: not applicable. For standard deviations of transfer efficiencies, please see Section 5 in the Supporting Information.

ErelayDouble (AC)Triple

To demonstrate the sensitivity of tripleFRET calculations and its power to dissect populations with different protein association patterns in biological systems, we mixed the samples together described in Table 3 in the same tube. Then energy transfer was measured by flow cytometry for the mixed sample. A representative dot plot and transfer efficiency histograms are shown in Figure 3. As can be seen on the transfer efficiency histograms, a single measurement of transfer efficiency allows discrimination of three distinct populations. When only EAB is measured, Specimens 1 and 6, Specimens 3 and 4, as well as Specimens 2, 5, and 7 cannot be separated from one another. When only EAC is analyzed, Specimens 1 and 2, Specimens 4 and 5 as well as Specimens 3, 6, and 7 show near identical transfer efficiency distributions. Total FRET efficiency is similar in Specimens 1 and 2 as well as in Specimens 4, 5, 6, and 7. The simultaneous calculations of several transfer efficiencies is needed for discrimination of specimens that show similar transfer efficiency distributions when only one FRET value is measured. The evaluation of all three FRET efficiencies allowed us to discriminate between seven differently labeled specimens in the same sample. The calculated transfer efficiency values for the identified specimens are displayed in Table 3. The transfer efficiency values measured in such a fashion were in good agreement with FRET efficiencies obtained from the specimens measured individually (data not shown).

Figure 3.

Three dimensional dot plot and histograms of energy transfer values determined from a mixture of seven doubly or triply labeled specimens after a single data acquisition step. The labeling schemes of the individual specimens can be found in Table 3.

Table 3. Labeling schemes and energy transfer efficiency values (%) measured for individual specimens after mixing and a single data acquisition
 Alexa Fluor 488Alexa Fluor 546Alexa Fluor 647
Specimen 1PertuzumabTrastuzumab
Specimen 2H76.5Trastuzumab
Specimen 3H76.5Pertuzumab
Specimen 4TrastuzumabPertuzumab
Specimen 5TrastuzumabH76.5Pertuzumab
Specimen 6PertuzumabTrastuzumabH76.5
Specimen 7H76.5TrastuzumabPertuzumab
FRET efficiencyABACBCRelayTotal
  1. For standard deviations of transfer efficiencies, please see Section 5 in the Supporting Information.

Specimen 3–
Specimen 59.89.633.02.912.4
Specimen 621.22.830.56.610.4
Specimen 713.54.544.25.510.2

TripleFRET in Three-Dye Systems with Different Spatial Distributions of Dyes

Lastly, we altered the labeling scheme (see Fig. 4) so that the three dyes could not colocalize on the same protein due to competition between antibodies. This way we either achieved a dye configuration where the transfer process from A to B is intermolecular (Sample 2) or dye B excited by energy transfer from dye A was not in close proximity of dye C (Sample 3), causing relay FRET to become minimal (Fig. 4). Transfer efficiency was calculated with different initial equation sets considering four scenarios: simultaneous relay and direct transfer from A to C; only relay transfer without direct transfer; only direct transfer without relay transfer; no relay or direct transfer (please see the Supporting Information for the equations used in the individual scenarios). Results and comparison with two-dye, dominantly intramolecular FRET values are summarized in Table 4. In the case of Sample 1, the scheme supposing direct and relay transfer to dye C gave the best approximation of energy transfer values from two-dye systems without neglecting any transfer processes. The same was true for Sample 2, where assuming only relay transfer neglected the substantial direct transfer process from dye A to C and supposing only direct-FRET underestimated energy transfer from A to B. However, for Sample 3, analysis involving simultaneous direct and relay transfer failed to give results with a physical meaning, as A to C transfer was found to be negative. Calculations with only relay transfer produced a relay-FRET value that was higher than the total energy transfer from A to C. Therefore, a scheme involving only direct transfer gave the best results, with physically plausible results obtained for all calculated transfer efficiencies. However, in this case a small but relevant amount of relay transfer was neglected, since total transfer was higher in the three-dye system than in a system with only dyes A and C. As we shall later discuss, in Sample 3 several different spatial distributions are measured at the same time, which causes calculations assuming a single, homogenous distribution to become inaccurate.

Figure 4.

Labeling schemes employed to provide alternative spatial distribution and possible transfer routes between fluorescently tagged antibodies. Bold arrows: primary transfer routes, dashed arrows: secondary transfer routes, arrows originating from circles: transfer routes potentially involved in relay-FRET. [Color figure can be viewed in the online issue which is available at]

Table 4. Comparison of measured transfer efficiencies (%) calculated with different initial equation sets for labeling schemes described in Figure 4
  1. The displayed EAB and EAC values are noncompetitive FRET values. Competitive FRET values are given in parenthesis where applicable. For standard deviations of transfer efficiencies, please see Section 5 in the Supporting Information.

Sample 1
Relay and direct FRET10.8 (9.9)9.6 (8.6)
Only relay-FRET10.831.53.312.6
Only direct FRET7.7 (6.8)12.6 (11.7)31.511.7
No relay or direct FRET7.731.513.3
In two-dye system10.810.225.010.2
Sample 2     
Relay and direct FRET2.7 (2.4)11.2 (10.9)
Only relay-FRET2.743.81.113.5
Only direct FRET1.5 (1.3)12.1 (12.0)43.812.0
No relay or direct FRET1.543.813.6
In two-dye system3.610.245.110.2
Sample 3     
Relay and direct FRET22.7 (23.6)–2.8 (–2.2)
Only relay-FRET22.622.45.02.8
Only direct FRET18.3 (17.8)3.4 (2.8)22.42.8
No relay or direct FRET18.522.43.5
In two-dye system20.


FRET measurements have gained wide acceptance as a means of following changes in molecular distance and association. However, the fact that FRET requires a close proximity of the donor and acceptor dyes has limited the dynamic range of these measurements. Furthermore, the spectral criteria of overlap between the emission spectra of donor and excitation spectra of acceptor meant that only two fluorescently labeled molecules were viewed at a time. Recent studies have shown that, by adding a third dye, the dynamic range of FRET can be extended via relay-FRET. With the addition of a new dye, new energy transfer pathways are opened, which may compete with the pathways already known from a two-dye system. The untangling of these pathways not only allows for a larger FRET range, but also has the potential to study the proximity relationship of three labeled molecules at the same time. Given the complexity of protein networks in signaling pathways, such an extension can be quite important in the quantitative description of protein interactions in signaling processes.

In this article, we present a relatively simple equation system with which all possible transfer efficiencies can be calculated in flow cytometry. Previous methods for measuring transfer efficiency between three fluorophores either relied on complicated fusion protein constructs (27, 40–42), were developed for dyes in solution and not adaptable for flow cytometers (15, 17, 23–25, 43), or needed a reference sample to determine the quantity of the donor dye (dye A) for proper calibration of transfer efficiencies. While the latter approach is also used and accepted as the simplest method for calculating transfer efficiency in two-dye systems (44), it carries the risk of skewed results if the quantity of the dye changes between samples. In experiments with fluorescently labeled antibodies, the probability for this is small as long as there is no competition between antibodies. However, when fluorescent protein coupled proteins are expressed in a cellular system, expression efficiency can vary from cell-to-cell and this effect is even more accentuated when multiple exogenous proteins are expressed (45). Therefore, we sought to develop a method, which does not rely on an external reference sample to calculate transfer efficiency. We identified and broke down to quantifiable components six different emission intensities in total, which, in a system of equations allow the individual FRET between each member of the system to be assessed, which in turn carries information about the relative spatial organization of the studied molecules or epitopes. Both uncorrected and competition-corrected transfer efficiencies were calculated to determine the apparent FRET of the dye system, while still obtaining the competition-free FRET values of a two-dye system. In our system, correcting for competition led to only minimal changes in transfer efficiency. However, in other systems closer proximity and/or larger spectral overlap between dyes could result in larger individual FRET efficiencies and therefore more significant competition, making this a valuable tool for generating FRET efficiencies comparable with values from two-dye systems.

In our experiments, we used Alexa Fluor 488, Alexa Fluor 546 and Alexa Fluor 647 fluorophores as dyes A, B, and C, respectively. There is sufficient spectral overlap between the excitation and emission spectra of these fluorophores to allow for all theoretically possible energy transfer routes. When measuring two-dye systems, evaluation with the classical intensity-based FRET and with the tripleFRET method gave comparable results. Also, FRET efficiencies obtained by the tripleFRET approach in three-dye systems for any dye-pair were in good agreement with the values measured and calculated for the corresponding two-dye system. However, when using the two-dye intensity-based method in a three-dye system, we measured significantly lower EAB and significantly higher EAC values compared with the corresponding two-dye systems. This can be attributed to the quenching of fluorophore intensity and augmentation of sensitized emission by the third fluorophore, so that distorted values are used as acceptor and donor fluorophore intensities during energy transfer calculation.

To demonstrate the sensitivity and the discrimination power of our approach, we have mixed, in a single tube, several distinctly labeled samples and have shown that following the acquisition of a single data set it is possible to resolve the various components of the population based on the correctly calculated individual FRET efficiencies relevant to the various molecular interactions characteristic of each label type.

The results also show that while our method is accurate, it fails to distinguish between different spatial distributions that produce near-identical transfer efficiency profiles. Without prior knowledge of the studied system, based solely on transfer efficiencies between pertuzumab and trastuzumab in two-dye systems, Sample 2 in Figure 4 can be assumed to follow the same spatial distribution as Sample 1. Only with the knowledge of antibody binding stoichiometry (i.e., just one recognized epitope per protein) can an accurate model be constructed. Theoretically, the two cases are distinguished by a slight increase in EAC and EBC from the presence of additional transfer routes; however, the contribution of these routes is mostly small and can be masked by measurement noise and biological variability.

As with all ensemble-oriented methods relying on signals from several fluorophores, individual FRET processes are averaged and are indiscernible from one another, that is, a mix of fluorophore populations displaying large and small FRET can produce a summed intensity signal indistinguishable from a homogeneous population with intermediate FRET efficiency, masking population heterogeneity, resulting in inaccurate FRET estimations (46). Sample 3 in Figure 4 demonstrates a spatial distribution where the dominant transfer processes characterized by EAB and EAC are competitive, and there is an independent process characterized by EBC. The assumption that relay transfer is equal to the product of EAB and EBC is still valid; however, due to spatial separation, one of the processes contributing to relay-FRET is significantly smaller than the dominant process characterized by EAB or EBC. In this case, calculations assuming parallel direct and relay-FRET with the measured dominant individual transfer values will overestimate quenching of EAB through dye C and contribution of relay-FRET to sensitized emission of dye C. This in turn results in underestimation of EAC. If the equation set assumes only direct transfer from A to C, then EAB is underestimated, EAC is overestimated and relay-FRET is neglected altogether. Ideally, the two secondary relay-FRET processes besides the dominant direct transfers should also be taken into account.

In most cases, various distinct molecular interaction schemes allow physically plausible EAB, EAC, and EBC values to be calculated from the same quenched donor and sensitized acceptor emission intensities. This in turn means that being able to calculate a given transfer efficiency does not guarantee that the FRET process is actually taking place at the molecular level. For instance, sensitized emission of dye C can be attributed to direct FRET between A and C, relay excitation through B or both. Based solely on intensity data we cannot distinguish between these cases or tell which one of them apply to a given situation. Even if multiple orientations are considered in FRET calculations, as long as the relative contribution of each to the ensemble FRET signal is not known, precise efficiency values cannot be calculated. The same effect is achieved when not all fluorophores participate in the transfer process, for instance, when three different proteins are labeled. The presence of single-dye species without transfer partners under such conditions is a problem even in traditional ensemble measurement types (47). Theoretically, an initial equation set can be developed to take multiple simultaneous distributions into account; however, the number of variables does not allow the equation set to be solved with the six measurable intensities. Therefore, accurate intensity-based calculations require prior knowledge about possible transfer routes, either from measurements in two-dye systems or known and/or limited spatial distribution of the imaged dyes (for instance rigid DNA strands that allow for only certain spatial orientations and limit the number of interacting dyes). Alternatively, single-molecule or lifetime measurements can help identify and characterize possible dye interactions in the studied system. Spectral analyses and unmixing may also be a viable route to determine the relative abundance of different dye species (42, 48). This limitation was not addressed in previous articles as either the methodology ensured that all three dyes were within interaction distance with limited possible relative orientations (all single-molecule imaging methods) or the chosen system was essentially restricted to certain relative orientations while ensuring uniform interaction of dyes (all measurements with DNA strands, fixed distance three-fluorophore constructs or multimers, where FRET is only possible in a given relative conformation of the imaged molecules). In such a fashion, either by chance or design, the restricted applicability of three-dye FRET measurements was not unmasked. It should also be noted that these considerations are only vital when precise absolute transfer efficiency values are needed and can be partially neglected when FRET is only used as a semiquantitative indicator (e.g., identification of distinct populations, relative conformation changes).

In previous articles, the three-dye system was mostly characterized with the total energy transfer of the donor to multiple acceptors. The higher total energy transfer values of the three-dye system over a two-dye system have been interpreted as an increase in the Förster critical distance, R0. Using Eqs. (2) and (3), Erelay can be given as follows:

equation image(24)

where r XY is the actual physical distance of the indicated dye pair and R0 XY is the corresponding Förster distance. The index ABC denotes the distances as interpreted for the whole relay transfer process. In a three-dye system, the AC distance as determined through relay-FRET (which is different from the Euclidean distance between A and C, since by definition, excitation first has to travel to B before being passed on to C) is equal to the sum of AB and BC distances:

equation image(25)

By combining Eqs. (24) and (25), the Förster critical distance for relay transfer can be given as:

equation image(26)

Therefore, the critical distance for relay-FRET is a function of the individual specific dye distances. Accordingly, the Förster distance calculated for relay-FRET is not an intrinsic property of the dyes determined by their spectra and quantum yields, but an arbitrary distance derived from distances calculated for two independent consecutive FRET processes. Thus in our view it is inappropriate to assign an R0 to relay-FRET, since it is only a mathematical construct that does not have a true physical meaning, and falsely gives the impression that it possesses the same type of spatial information as the distances calculated from the individual two-dye FRET efficiencies in characterizing the three-dye system. In this sense, relay-FRET should be used as a qualitative indicator of dye interaction in three-dye systems, but not as the basis for quantitative distance measurements.


The long-standing perception of FRET as a process confined to measuring two fluorophores is gradually being revised with the development of novel methods for monitoring multiple fluorophores. Most recently, several techniques are emerging for detecting FRET in four dye systems (49–51). However, even the simpler three-dye methods have not become widespread, chiefly because of unique instrumentation and sample preparation requirements. In this article, we presented a relatively easy-to-implement method, which can be used with commercial flow cytometers. Solutions are given for an initial equation set that allows FRET calculation in a three-dye system as is, without the need for an external reference sample to quantify unquenched donor intensity. We have shown that the performance of tripleFRET with respect to sample discrimination and reproduction of FRET efficiency values of two-dye systems is equivalent to that of three-dye single molecule FRET microscopy methods, and can be applied to FRET investigations of cell surface proteins labeled with fluorescently tagged antibodies. Furthermore, limitations arising from spatial distributions that can influence the interpretation of experimental data and until now which have not been discussed in the literature was addressed. This should help researchers design and conduct FRET experiments to harness the information gained by the addition of a third dye to conventional two-dye systems.