INTRODUCTION

Top Abstract Introduction Methods Results Discussion References

Fluorescence resonance energy transfer (FRET) microscopy is a technique used for quantifying the distance between two different fluorophores (Clegg, 1996). FRET involves the transfer of energy from a fluorescent donor in its excited state to another excitable moiety, the acceptor, by a nonradiative dipole-dipole interaction (Lakowicz, 1983). FRET requires that 1) the donor be fluorescent and of sufficiently long lifetime, 2) the transfer not involve the actual resorption of light by the acceptor, 3) the donor molecule's fluorescence emission spectrum overlaps (to some extent) the excitation spectrum of the acceptor molecule, and 4) the distance between the donor and acceptor molecules is small (1-10 nm). The dependence of the energy transfer efficiency on the donor-acceptor separation provides the basis for the utility of this phenomenon in the study of cell component interactions. FRET does not require that the acceptor be fluorescent, but the methods of FRET measurement requiring three filter sets presented in this report do require that the acceptor be fluorescent and that the acceptor not quench the donor by any mechanism other than FRET.

In steady-state FRET microscopy FRET can be detected by exciting the labeled specimen with light of wavelengths corresponding to the excitation spectrum of the donor and detecting light emitted at the wavelengths corresponding to the emission spectrum of either the donor and/or the acceptor. When FRET occurs, the donor emission is decreased and the acceptor emission is increased (sensitized emission). Various methods have been used to measure FRET from the changes in donor and acceptor emission. Proper use of FRET measurements to characterize molecular interactions requires that corrections be made for 1) cross talk (the detection of donor fluorescence through the acceptor emission filter and the detection of acceptor fluorescence through the donor emission filter), 2) the situation 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. This report presents a simple method to correct for each of these parameters. The method requires a minimum of spectral information and can be readily implemented on a microscope or in a fluorometer. Corrections for background fluorescence, autofluorescence, and photobleaching may also be required and are applied before using any of the methods discussed below.

	METHODS

Top Abstract Introduction Methods Results Discussion References

Cell preparations and microscopic measurement of FRET

COS cells co-transfected with Bcl-2 and flag epitope-tagged Beclin (Liang et al., 1997, submitted for publication) were used in the studies described in this paper. Beclin is a recently discovered coiled-coiled Bcl-2 interacting protein located on chromosome 17q21. Bcl-2 is an anti-apoptotic protein localized in the outer mitochondrial membrane whose activity is modulated by Beclin. The target proteins were labeled with donor and acceptor by fluorochrome conjugated antibodies specific to the target proteins. Wild-type and mutant Flag epitope tagged Beclin were labeled with donor fluorochrome (FITC) and Bcl-2 was labeled with acceptor fluorophore (rhodamine). As a control for these studies we labeled the endoplasmic reticulum Ca²⁺-ATPase (SERCA) with donor (FITC) and Bcl-2 with acceptor (rhodamine) in the same cell type.

FRET was detected by exciting the labeled specimen with light of wavelengths corresponding to the absorption spectrum of the donor and detecting light emitted at the wavelengths corresponding to the emission spectrum of the acceptor. FRET manifests itself by both quenching of donor fluorescence in the presence of acceptor and in sensitized emission of acceptor fluorescence. FRET microscopy was performed as previously described (Liang et al., 1993). The donor (FITC) filter set consisted of [excitation (ex) = 480-500 nm; dichroic mirror (dm) = 510 nm; emission (em) = 515-555 nm]. The acceptor (rhodamine) filter set consisted of [ex = 546/40 nm; dm = 580 nm; em = 590 nm long pass]. Images obtained with these two filter sets were used to directly quantify the intensities of each fluorophore. The FRET filter set consisted of [ex = 450-490 nm; dm = 580 nm; em = 580 long pass]. The signal recorded from this filter set is the FRET signal that arises from energy that has been transferred from FITC to rhodamine molecules. A background value was determined from a region in each image that did not have any cells. The background value was subtracted from the foreground value from a region within a cell. A mapping program written in-house was used to map fluorescent cells and quantify the intensity within each cell.

General equations for FRET

All the methods of FRET measurement discussed here use one or more of three filter sets, which are termed the Donor, FRET, and Acceptor filter sets. These filter sets are designed to isolate and maximize three signals: the donor fluorescence, the acceptor fluorescence due to FRET, and the directly excited acceptor fluorescence, respectively. The excitation filters for the donor filter set and the FRET filter set are either the same filter or two matched filters. The emission filters for the FRET and Acceptor filter sets are either the same filter or matched filters. Neutral density filters may be used to match the signals from the three filter sets to the dynamic range of the detector.

In previous publications describing analysis of FRET data authors have tended to use different symbols for the various fluorescence signals. Those symbols will be used when appropriate. In addition, a common set of symbols is defined which represents and replaces most of the previously used symbols and provides a common vocabulary for comparison of the various methods. Two- and three-letter symbols are defined to represent the signals using the type of filter set (Donor, FRET or Acceptor), the fluorochromes present in the sample (donor only, acceptor only, or both donor and acceptor) and the signal from either just the donor or acceptor when both are present in the sample. Each symbol starts with an uppercase letter representing the filter set, D for the Donor filter set, F for the FRET filter set, and A for the Acceptor filter set. The second letter is lowercase and indicates which fluorochromes are present in the specimen, d for donor only, a for acceptor only, and f for both donor and acceptor present (so FRET is possible). In the three-letter symbols, the third letter is lowercase and indicates the signal from only one of the fluorochromes when both fluorochromes are present. For example, if the third letter is d, this would indicate the donor component of the combined signal, while a would indicate the acceptor component of the combined signal. The donor- or acceptor-only signals represented by the three-letter symbols cannot be measured directly unless the acceptor is not present when donor is to be measured, and vice versa. (This is equivalent to the situation where there is no cross talk of that type.) A second type of three-letter symbol consists of a three-letter symbol of the first type with a bar over it and is used to indicate the signal that would exist if no FRET occurs. Tables 1-3 list each of the symbols used in the analysis of the FRET data along with the filter set, fluorochromes present, and an explanation of what is measured under each condition.

As an example, Df is the signal with the Donor filter set and both fluorochromes present. Df = Dfd + Dfa where Dfd is the donor signal and Dfa is the acceptor signal (i.e., Dfa represents the acceptor fluorescence with the Donor filter set with both fluorochromes present). Dfd =   FRET1 where is the donor signal that would have existed if no FRET occurred (as if no acceptor were present) and FRET1 is the loss of donor signal due to FRET (because acceptor was in fact present). Dfa will be zero if the wavelengths of emission of the acceptor do not overlap the wavelengths of transmission of the emission filter of the Donor filter set, or if the excitation spectrum of the acceptor does not overlap the wavelengths of transmission of the excitation filter of the Donor filter set. Expressing Df, Ff, and Af as their donor and acceptor components yields Eqs. 1. 

(1a)

(1b)

(1c)

Ffd is nonzero only if the donor emission spectrum overlaps the wavelengths of transmission of the acceptor emission filter. Afd is nonzero if the donor is excited and the Acceptor filter set detects its emission. Thus, the terms Dfa, Ffd, and Afd are all due to cross talk; any one of these terms will be zero if its particular type of cross talk is not present.

In addition to these symbols, we also define a set of two-letter symbols for signals arising from specimens containing either only donor or only acceptor fluorochrome. Dd, Fd, and Ad represent signals obtained when only donor is present, while Da, Fa, and Aa signify signals obtained when only acceptor is present. These six measured values characterize the fluorophores' excitation and emission spectra including cross talk (Fd, Ad, Fa, and Da represent cross talk) and characterize the filter sets by providing the signal with each filter set from the same specimen. For example, Ffd/Dfd is the ratio of two quantities that are not directly measurable. However, this quantity can be measured as the ratio Fd/Dd = Ffd/Dfd. Ffd/Dfd is the ratio of the donor signals obtained with the FRET and Donor filter sets from a specimen with both donor and acceptor present. Fd/Dd is also the ratio of the donor signals with the FRET and Donor filter sets from a specimen with only donor present. The FRET that may occur in the specimen with both donor and acceptor does not affect the Ffd/Dfd ratio because the same fractional loss due to FRET occurs with both filter sets. Rearranging the equation yields Ffd = Dfd (Fd/Dd). By using similar logic Dfa = Ffa (Da/Fa), and Afd = Dfd (Ad/Dd). In the latter case the emission filter is the same between the two filter sets. Substituting these three relationships into Eqs. 1 yields Eqs. 2. 

(2a)

(2b)

(2c)

Each of the six terms on the right sides of Eqs. 2 can be expressed as two components: a FRET component and a non-FRET component. As in the example above, Dfd can be expressed as the donor emission that would occur in the absence of FRET, minus the loss of donor emission due to FRET (Dfd =   FRET1). Dfd originates in the equation for the Donor filter set, Eq. 2 a. In Eq. 2, b and c, the donor contributions are also expressed in terms of Dfd. Afa originates in the equation for the acceptor filter set. The next step is to express the acceptor contributions in Eq. 2, a and b in terms of Afa. Afa has two components, the component representing the signal as if no FRET occurred, , and the component due to FRET, temporarily termed AfaFRET. Ffa has two components, the component representing the signal as if no FRET occurred, , which equals (Fa/Aa) (by logic similar to the logic above), and the component due to FRET, which is expressed as G · FRET1 (the value G will be explained below). G · FRET1 is expressed in terms of the loss of donor signal due to FRET (FRET1). The acceptor FRET signals in the other two equations will be expressed in terms of G · FRET1. Dfa has two components, the component representing the signal as if no FRET occurred,  =  (Da/Fa) =  (Da/Aa) by substitution and the component due to FRET = G · FRET1 (Da/Fa) expressed in terms of the component due to FRET of Ffa (which is G · FRET1). In order to express AfaFRET in terms of G · FRET1 it is important to note that the difference between the signals is the excitation filter used and that the FRET signal is proportional to the excitation of the donor (and not the direct excitation of the acceptor). The ratio of measured values that relates the excitation of the donor with the FRET and Acceptor filter sets is Ad/Fd. Therefore, AfaFRET = G · FRET1 (Ad/Fd). This logic is slightly different from the logic above since a component of the acceptor signal depends on the donor excitation. Equations 3-6 summarize these results.

(3)

(4)

(5)

(6)

Substituting Eqs. 3-6 into Eqs. 2 yields Eqs. 7. 

(7a)

(7b)

(7c)

In Eqs. 7, all the terms with ratio multipliers (Da/Aa, Fd/Dd, etc. are the ratio multipliers) are due to cross talk. None, some, or all of these cross talk terms may be zero for a given choice of fluorochromes and filters. However, the solution of this most general case can be processed to give the correct answer for any choice of fluorochromes and filters, whatever the cross talk situation.

G is the factor relating the loss of donor signal due to FRET with the Donor filter set to the increase in acceptor signal due to FRET with the FRET filter set. where QY_a and QY_d are the quantum yields of the acceptor and donor, respectively, and _a is the fraction of the acceptor fluorescence transmitted by the acceptor emission filter. Similarly, _d is the fraction of the donor fluorescence transmitted by the donor emission filter. T_F and T_D are the fractional transmissions (or percent transmissions) of the neutral densities used in the two filter sets. The fraction of fluorescence transmitted is equal to the area under the product of the fluorescence emission spectrum, and the transmission spectrum of the emission filter divided by the area under the emission spectrum. The bit-mapped graphics program Adobe Photoshop was used to estimate the areas under the various curves by counting pixels with the histogram function.

Equations 7 contain three unknowns (, FRET1, and ), and whose solution is given by Eqs. 8. 

(8a)

(8b)

(8c)

FRETN: A fully corrected measure of FRET

The measure of FRET normalized for the concentrations of donor and acceptor and derived from Eqs. 8 is termed FRETN and is given in Eq. 9.

(9)

Equation 9 also indicates the proportional relationship between FRETN and the concentrations of the interacting and noninteracting species. In Eq. 9, [bound] represents the concentration of interacting pairs of the donor labeled species and the acceptor labeled species, and [total d] and [total a] represent the total concentrations (interacting and noninteracting) of the donor and acceptor labeled species, respectively. FRET1 is proportional to the FRET signal from the specimen, which in turn is proportional to the number of interacting pairs of donor and acceptor. is the donor signal that would take place if no FRET occurred and is therefore proportional to the total concentration of donor. is the acceptor signal that would take place if no FRET occurred and is therefore proportional to the total concentration of acceptor. All three values, FRET1, , and are corrected for cross talk and have fully separated the FRET signal from the non-FRET signal. FRETN is a measure of FRET, which has the further correction that it is normalized for the donor concentration and acceptor concentration. FRETN is not equal to or proportional to the equilibrium constant, K_eq, but does look similar to K_eq for interaction between the donor labeled species and the acceptor labeled species (cf. Eq. 10).

(10)

where [bound] is as before, and [free d] and [free a] are the concentrations of the noninteracting donor labeled species and noninteracting acceptor labeled species, respectively. The relation between FRETN and K_eq is monotonic; that is, whenever K_eq increases so does FRETN. A sketch of the relation between FRETN and K_eq is shown in Fig. 1. The shape of the curve relating FRETN and K_eq is known but absolute values are not known. FRETN is a relative measure of K_eq even though the exact relation between the two is unknown. K_eq is the best measure of the interaction intensity of the donor labeled species with the acceptor labeled species. FRETN is not equal to or proportional to K_eq, but it is a relative measure of K_eq, and therefore of the interaction intensity. FRETN makes the best use of the data collected using the three filter sets described. Any better measure would require substantially more data.

View larger version (27K): [in this window] [in a new window]   FIGURE 1   Relationship between FRETN and Keq. See text for details.

With the proper choice of filters, the values of Da and Ad can be effectively zero for fluorescein and rhodamine as the donor and acceptor, respectively. In this case the calculation of FRETN is greatly simplified, as shown in Eq. 11.

(11)

In Eq. 11 G occurs only as a constant multiplier of FRETN and may be assigned an arbitrary value (e.g., G = 1) instead of being calculated or measured. If the two cross talk values, Ad and Da, are zero, then this formula for FRETN (Eq. 11) separates the FRET and non-FRET signal components, is corrected for the remaining cross talk, and is normalized for the concentrations of donor and acceptor. This is the same FRETN as in Eq. 9 but adjusted to account for the simpler cross talk situation, and is therefore a relative measure of the K_eq for the interaction as described above. The numerator of this formula for FRETN is the same as the corrected FRET value used in the MicroFRET method (Youvan et al., 1997). MicroFRET is not normalized for the concentration of either donor or acceptor.

Calculating FRETN under all cross talk situations

The first step in the calculation was to screen the data for aberrant data. The original intent of this step was to determine the occurrence of outliers. The screening method consisted of dividing the data into three groups according to which fluorochromes were present in the specimen: 1) group f if both donor and acceptor were present; 2) group d if only donor was present; and 3) group a if only acceptor was present. FRETN and Ffa/Dfd were calculated for all possible combinations of one specimen from each of the three groups. "Outliers" were identified by negative values for either FRETN or Ffa/Dfd. Each combination that produced a negative value of FRETN or Ffa/Dfd was flagged. If all of the combinations involving a particular specimen were flagged, that specimen was removed from its group and from further data analysis. If only some of the combinations involving a particular specimen were flagged, the specimen was taken as an ordinary outlier.

The second step was to calculate the required ratio multipliers for each of the remaining specimens in group d and then calculate the average across specimens of the ratio multipliers. For example, the ratio multipliers required from group d are Ad/Fd and Fd/Dd. If the denominator of a ratio for a particular specimen is zero, the entire ratio was set to zero. This is not meant to be a mathematical truth, but empirically it generates the correct solution of Eqs. 7 for the cross talk situation in which the value in the denominator would be zero. Ad/Fd and Fd/Dd were calculated for each specimen and then the average of Ad/Fd and the average of Fd/Dd were calculated across all of the donor group of specimens. Each of the ratio multipliers used to calculate FRETN is self-normalizing for concentration since the numerator and denominator are measurements of the same specimen. Thus, the use of these ratios removes the concentration-dependent variability from the calculation, which might result from variation in the concentration of donor in the donor-only specimen and variation in the concentration of acceptor in the acceptor-only specimen. This true reduction in noise is exploited by using the averages of the ratio multipliers instead of the averages of the measured values in the calculation of FRETN. The same process is applied to the specimens in group a to get averaged values of the required ratio multipliers Fa/Aa, Da/Aa, and Da/Fa.

The third step is to use the values of the averaged ratio multipliers to calculate FRETN for each specimen in the FRET group and calculate the mean and standard deviation of FRETN. A software program developed in-house carried out the entire three-step calculation. The same calculation is applied to the data from the suspected interacting specimen and the noninteracting control. The resulting FRETN values were compared by means of a Welch's t-test to evaluate the significance of the difference between the experimental and control specimens. If a noninteracting control were not available, it would be possible to assume that the mean of FRETN for the noninteracting control (if it existed) is zero and compare the suspected interacting data to the zero control with a t-test. However, it should be noted that incorrect conclusions might be reached if a real noninteracting control would in fact have significant FRET.

Other means of calculating FRETN

There are two alternative derivations for FRETN that produce the same values for FRETN but which are (at least superficially) different from the solution of Eqs. 7. The first of the alternative ways is an extension of formulation used to develop the FCET method (Trón et al., 1984). The second of the alternative ways is presented for completeness.

The first of the alternative methods for calculating FRETN is derived from Eqs. 7 by substituting · FRET2 for FRET1 in all three equations yielding Eqs. 12. This produces an explicit recognition of the dependence of the FRET signal on the concentration of donor.

(12a)

(12b)

(12c)

The solution of equations 12 is given in Eqs. 13. 

(13a)

(13b)

FRET2 is already normalized for the concentration of donor so FRETN is given by Eq. 14.

(14)

The second of the alternative means of calculating FRETN is derived from Eqs. 7 by substituting ·  · FRET3 for FRET1 in all three equations producing Eqs. 15. This produces an explicit recognition of the dependence of the FRET signal on the concentrations of donor and acceptor.

(15a)

(15b)

(15c)

FRET3 is already normalized for the concentrations of both donor and acceptor and is therefore equal to FRETN as expressed in Eq. 16. Solving Eqs. 15 for FRET3 produces the same formula for FRETN as the solution of Eqs. 12. The solution of Eqs. 7 produces the same values for FRETN as produced by Eqs. 12 and 15, although the formula for FRETN is (at least superficially) not the same. Equation 16 expresses the equality of the numerical values of FRETN calculated via FRET1, FRET2, and FRET3.

(16)

	RESULTS

Top Abstract Introduction Methods Results Discussion References

The interaction of the anti-apoptotic protein Bcl-2 with Beclin, a candidate novel tumor suppressor gene, was examined using FRET (Liang et al., 1993; submitted for publication 1997). The donor and acceptor were fluorescein and rhodamine, respectively.

Cos cells co-transfected with pSG5/Flag-Beclin and pSG5/Bcl-2 were labeled with donor (fluorescein conjugated) anti-flag and acceptor (rhodamine conjugated) anti-Bcl-2 antibodies, respectively. As a negative control, cells were labeled with donor (fluorescein conjugated) antibody against the endoplasmic reticulum Ca²⁺-ATPase (SERCA) and acceptor (rhodamine conjugated) anti-Bcl-2 antibody. As shown in Table 4, there is a statistically significant difference in the FRET signal (FRETN) between Bcl-2 and Beclin versus Bcl-2 and SERCA. FRETN was also significantly greater in the case of Bcl-2 and Beclin versus Bcl-2 and mutant Beclin (Table 5). In these studies, the donor excitation filter was a 490/20 nm bandpass and the donor emission filter was a 515-555 nm bandpass. The acceptor excitation filter was a 546/40 nm bandpass, and the emission filter was a 590 nm longpass. The ratio of the quantum yields of the acceptor to donor was 0.25 (Haugland, 1996). The fractional transmissions of the donor and acceptor emission filters were 0.38 and 0.40, respectively. The percent transmissions of the FRET and Donor filter set neutral density filters were 100 and 3.2, respectively, for the experimental and the SERCA negative control (G = 7.42) and 20 and 1, respectively, for the mutant Beclin negative control (G = 4.75).

In Table 4, the p value of the t-test of the significance of the difference in FRETN between the Bcl-2 and Beclin versus Bcl-2 and SERCA is not very sensitive to the value of G over a range of 0.1 to 10.0 times the true value (data not shown). Therefore, using rough estimates of the quantum yields and the fractional transmissions of the emission filters should not be a problem. (G is the factor relating the loss of donor signal due to FRET with the Donor filter set to the increase in acceptor signal due to FRET with the FRET filter set.)

Other methods to measure FRET using three filter sets

Recently, Youvan et al. (1997) published a method for analyzing FRET that uses three filter sets and is termed MicroFRET. The FRET value calculated using this method is termed "corrected FRET" and is represented by F^c. The formula for the calculation of FRET using the MicroFRET method, in notation of the present report, is shown in Eq. 17.

(17)

F^c does separate the FRET signal from the non-FRET signal if Ad and Da are effectively zero. However, if Ad and Da are not zero, then F^c does not correct for the resulting cross talk and the FRET versus non-FRET signals are not separated. Ad and Da can often be made effectively zero by appropriate choice of fluorochromes and filter sets. F^c can be normalized for the concentration of donor by using F^c/Df, which is approximately normalized for the concentration of donor. Similarly F^c/(Df · Af) would be approximately normalized for the concentrations of both donor and acceptor (see Tables 1 and 2). Other authors have successfully used different three filter set methods of measuring FRET (e.g., Mittler et al., 1991; Liang et al., 1993; Szöllösi et al., 1987; Trón et al., 1984).

Measurement of FRET using two filter sets

In addition to measurement of FRET using the three-filter set/three specimen approach described above, it is possible to measure FRET using only two filter sets. The use of only two-filter sets effectively means that only two unknowns can be determined. Since there are three unknowns in Eqs. 7, it would seem that a method using two-filter sets would result in less accurate and less stringent determination of FRET than the three-filter sets/three specimen method. In fact, this is the case when the concentration of donor and acceptor are not correlated. However, if the concentration of donor and acceptor are correlated, calculation of FRET using two-filter sets can produce equivalent results to measurement of FRET with three-filter sets.

The simplest measure of FRET using two-filter sets is Ff/Df, which does not separate FRET from the non-FRET signal, nor does it correct for cross talk. It does, however, make a partial normalization for the concentration of donor. The normalization is partial due to the lack of full correction for cross talk and lack of separation of the FRET and non-FRET signals of Df. (Ff/Af is an analogous measure using the Acceptor filter set in place of the Donor filter set.)

A method for calculating FRET using two-filter sets and which does correct for cross talk, but does not separate FRET and non-FRET signals, is as follows. Note that in Eqs. 2, a and b there are two unknowns, Dfd and Ffa. Solving for Dfd and Ffa and then taking their ratio, Ffa/Dfd yields Eq. 18.

(18)

This result is corrected for cross talk and is applicable even if one or more of the cross talk terms (Fd, Da, and Fa) is zero. In the case where Fa = 0, it is necessary to set Da/Fa = 0 to obtain the correct solution. While this measure of FRET is now corrected for cross talk and has improved normalization for the concentration of donor (Dfd is a better measure of donor concentration than Df), it is not normalized for the concentration of acceptor nor does it separate the FRET and non-FRET signals. Ff/Df and Ffa/Dfd both detect FRET with a very high significance (low p values) in Tables 4-6, implying that in these data a) the correction for cross talk is not required, b) the separation of FRET and non-FRET signals is not required, and c) normalization for acceptor concentration is not required. Other data may require methods that provide these corrections.

Any method using two-filter sets to calculate FRET must make an assumption about the missing data, which would have been provided by the third filter set. Ff/Df and Ffa/Dfd are missing data about the concentration of acceptor. The two-filter set method therefore makes a tacit assumption about the acceptor concentration. However, it is possible to make an explicit assumption about the missing data, and, if the assumption is valid, such a two-filter set method would be optimal. When using Donor and FRET filter sets, one possible explicit assumption about the acceptor concentration is that it is always a constant, S, times the donor concentration. If donor-only and acceptor-only specimens can be prepared that have the ratio of the acceptor concentration to donor concentration equal to S, then measuring those specimens with two-filter sets produces values Dd', Da', Fd', and Fa' where the two-letter symbols are as before and the prime indicates that the measurements were made with the defined relation between acceptor and donor concentrations. In practice, it is unlikely that S will be known; however, it would not be necessary to know S if specimen preparation were consistent, such that any variations in donor and acceptor concentrations only caused changes in their respective signals, which were smaller than the FRET signal to be measured. Empirically this condition may be common, since methods using two-filter sets have been used successfully with a tacit assumption about the missing data. Rewriting Eqs. 7, a and b with the primed symbols and at the same time replacing FRET1 with FRET4 to indicate a different analysis method yields Eqs. 19. 

(19a)

(19b)

In Eq. 19 a the term (Da'/Aa') may be replaced by (Da'/Dd') because the acceptor signal is assumed to be proportional to the donor signal with the same filter set. The proportionality constant for the Donor filter set is Da'/Dd'. Similarly, in Eq. 19 b, the term (Fa'/Aa') may be replaced by (Fd'/Dd')(Fa'/Fd'), which equals (Fa'/Dd'). Making these substitutions in Eqs. 19 yields Eqs. 20. 

(20a)

(20b)

Equations 20 are two equations with two unknowns, and FRET4. Solving for the unknowns yields Eqs. 21. 

(21a)

(21b)

Under these conditions, the optimal measure of FRET with two-filter sets is then FRET4/, which is corrected for cross talk, for the separation of the FRET and non-FRET signals and is normalized for the concentration of the donor under the assumption that the acceptor concentration is a constant proportion of the donor concentration.

(22)

In this measure of FRET there are ratio multipliers that are not self-normalizing in the sense that the numerator and denominator refer to different specimens. However, given the assumption that the donor and acceptor concentrations are correlated, the donor signal may at least partially normalize the acceptor signal. By choice of fluorochromes and filters it is often the case that Da is zero, and in that case the result simplifies to Eqs. 23 and 24.

(23a)

(23b)

(24)

In Eq. 24, FRET4/ is the same as in Eq. 22, but adjusted for the simplified cross talk situation. In this case G is not a simple multiplier of the measure of FRET and therefore must be determined before calculating FRET4. This is an interesting contrast to the method using three-filter sets in which when Da and Ad were taken as zero, the value of G could be assigned arbitrarily. In Table 5, where the more stringent negative control was used, FRET4/ failed to detect the FRET signal (p = 0.053 > 0.05). The analog to FRET4/ in the method using three-filter sets is FRET1/, which did detect FRET but which also showed a very large increase in p value over the case with the less stringent negative control (Tables 4 and 5).

Methods to calculate FRET using one-filter set

If only one filter set is to be used for measurement of FRET, it makes sense to choose the FRET filter set since it is designed to be the most sensitive to the FRET signal. The value Ff could be used with no attempt at correction. Ff could be partially normalized by dividing by Fd or (Fd · Fa) (see Tables 4-6 for examples). In the study represented in Table 4, even Ff, the uncorrected measurement using a single filter set, detected a difference in FRET between the interacting versus noninteracting donor and acceptor molecules. One-filter set methods have been used successfully (e.g., Erickson and Cerione, 1991; Shapiro and McCarty, 1990; Matayoshi et al., 1990).

Interaction-sensitive versus single-distance model for FRET

All of the methods described above are designed to measure FRET between molecules that are free to diffuse independently of each other and interact according to their specific K_eq for interaction. This is called the interaction-sensitive model because interaction between the donor labeled molecules and the acceptor labeled molecules is reflected in an increase in FRET (Lakowicz, 1983). In the interaction-sensitive model, the donor and acceptor do not bind directly to each other but are attached to two distinct molecules. Distinct molecules interact and bring the donor and acceptor closer together. Therefore, it is possible that the donor and acceptor are not at a fixed distance apart from one another, even in an interacting pair of molecules, primarily due to the flexibility of the intervening molecular structure. Another condition of the interaction-sensitive model is that, as observed above, the donor labeled species and the acceptor labeled species will not in general have the same concentration.

In addition to the interaction-sensitive model, there is a single-distance model in which the donor and acceptor occur only in covalently bound pairs (Lakowicz, 1983). In the single-distance model, the distance between paired donor and acceptor molecules is assumed to be fixed within a given pair, the fixed distance is assumed to be the same for all pairs, and the concentration of donor is equal to the concentration of acceptor. Because there are fewer unknowns, the same measured data can better characterize the FRET signal.

The most popular equation used to measure distance with FRET (Clegg, 1996) is:

(25)

where E is the efficiency of FRET (defined as number of energy transfer events divided by the number of photons absorbed by the donor), R₀ (Förster critical distance) is the distance at which E is 0.5, R is the distance between donor and acceptor, and F_DA and F_D are the donor fluorescence in the presence and absence of acceptor, respectively. F_DA and F_D are normalized for their respective concentrations of donor. R₀ must be determined in a separate experiment and requires knowledge of the spatial orientation of the donor and acceptor dipoles.

Equations 8, a and b can be used to calculate accurate values of the efficiency of energy transfer and the distance between the covalently bound donor and acceptor using the single-distance model. All three filter sets must be used, even though results from only two of the three parts of the solution are used. To calculate 1  (F_DA/F_D) note that F_DA is analogous to Dfd and F_D is analogous to . Also note that F_DA and F_D in the original formulation refer to different specimens, but Dfd and refer to the same specimen. Therefore, the ratio of Dfd and is already normalized for the concentration of donor, so (F_DA/F_D) = (Dfd/). The values and Dfd are corrected for cross talk, for the separation of the FRET and non-FRET signals and their ratio is normalized for donor concentration since they refer to the same specimen and the same filter set. Therefore:

(26)

(27)

(28)

Therefore, given R₀, E and R can be calculated from Eq. 29.

(29)

Since in the single-distance model the donor and acceptor concentrations are equal, the model can be formulated having only two unknowns and can therefore be analyzed with a system of two equations based on two filter sets (in this case the Donor and FRET filter sets will be used). Additional information is required for the two filter set method: the filter sets must also be used to measure donor-only and acceptor-only specimens which have known concentrations of donor and acceptor (or at least the ratio of concentrations must be known). Equations 23a and b, which express a two-filter set method for the interaction sensitive model, apply also in the present case of the single-distance model. The ratio, S, of acceptor concentration to donor concentration is known to be one in the single-distance model. Thus, the same solution applies and E = FRET4/.

These measures, FRET1/ and FRET4/, allow calculation of correct values of E and R in the single-distance model and are useful measures of FRET in the interaction-sensitive model when the concentrations of donor and acceptor are correlated. E and R are not well defined in the interaction-sensitive model.

	DISCUSSION

Top Abstract Introduction Methods Results Discussion References

We present methods to measure FRET, which can be used to detect the interaction between two distinct proteins inside single cells. There were a number of reasons for undertaking the analysis described in this paper. First, there is increasing interest in the detection of interactions between intracellular molecular species and FRET provides a powerful technique for achieving this goal. Second, a number of donor/acceptor pairs suffer significant cross talk. For example, fluorescein and rhodamine are a commonly used donor/acceptor pair and many of the commonly available fluorescein filter sets will excite rhodamine and allow its detection. This type of error in FRET measurement has not been accounted for in the flow cytometry energy transfer (FCET) method (Trón et al., 1984). Third, accurate measurement of FRET should not only correct for cross talk, but also normalize for the dependence of FRET on the concentration of the donor and acceptor. Acceptor concentration normalization is not done in the FCET method. Fourth, the use of FRET for the detection of interactions between fluorescently labeled molecules should use a minimal amount of spectral information so that the method can be readily implemented using a fluorescence microscope or other fluorometer.

We examined the interaction of the anti-apoptotic protein Bcl-2 with a recently identified candidate tumor suppressor gene Beclin. Interactions between Bcl-2 and Beclin were examined because previous studies employing yeast-two-hybrid approaches have indicated a high degree of interaction of these proteins (Liang et al., 1997, submitted for publication). As controls, we examined the level of interaction assessed by FRET between Bcl-2 and a mutant Beclin protein which is known not to interact with Bcl-2, and between Bcl-2 and the endoplasmic reticulum Ca²⁺-ATPase (SERCA). To our knowledge this is the first time that proteins constituting components of the apoptotic pathway have been examined at the single cell level and that proteins involved in the regulation of apoptosis have been shown to interact with a protein in the tumorigenic pathways (Liang et al., 1997, submitted for publication). In previous work (Liang et al., 1993) has used FRET to detect intracellular molecular interactions using a different three-filter set method that normalizes for both donor and acceptor concentrations.

The data in Table 4 display the level of FRET calculated using the various methods described in this paper. All of the methods demonstrate a significant difference (p < 0.05) in the level of FRET between the suspected interacting proteins and the presumed noninteracting control proteins. We employed two different types of controls. The first was to determine the level of FRET in noninteracting proteins whose distribution was spatially distinct in cells (e.g., Bcl-2 is primarily localized to mitochondria and SERCA is primarily localized to the ER). The second was to determine the FRET between two presumed noninteracting proteins that are precisely co-localized in the cell (i.e., Bcl-2 and the mutant Beclin). These results are shown in Table 5. In the first set of controls, FRET is not anticipated due to the spatial segregation of donor and acceptor. In the second control, both proteins are primarily localized to the mitochondria and FRET might occur either due to diffusion or due to an interaction, which failed to produce the usual physiological response to the interaction. The second type of control is better than the first type in that it is much less likely to produce a false positive detection of FRET. In Table 5 only those measures of FRET having some degree of normalization for concentration of donor or for both donor and acceptor show a significant difference in FRET between the experimental and control. Therefore, in situations where the negative control may exhibit FRET and the donor and acceptor concentrations are variable, it is important to normalize the FRET data for the concentration of one or both the donor and acceptor. This will enhance the sensitivity of the FRET measurement to the interaction of the donor and acceptor.

There are two types of error in FRETN that cannot be corrected for using the three-filter set/three specimen method described in this manuscript. The first is that interaction of labeled with unlabeled molecules could occur. This interaction would not lead to FRET and would cause an error dependent on the ratios of labeled to unlabeled molecules. This error can be minimized by having a large excess of labeled over unlabeled species. In cases in which the labeled species are introduced by transfection of vectors with constitutive promoters, such large excess is likely. The second type of error results from FRET between any donor and acceptor that are not part of the same interacting pair. This case might arise if the donor and acceptor molecules moved close enough for FRET to occur in a transient fashion due to diffusion. It would be possible to estimate the size of the error due to FRET between noninteracting donor and acceptor if noninteracting species had the same spatial distribution as the interacting species under study. This error could be estimated measuring FRETN for a control specimen created with appropriately labeled noninteracting species.

When the values of FRETN for experimental and control specimens are compared, a difference between experimental and control in the ratio of total acceptor concentration to total donor concentration ([total a]/[total d]) is a possible source of error in judging the difference in K_eq between experimental and control. This possible error results from the fact that FRETN is not equal to or proportional to K_eq for interaction. FRETN is tabulated in Table 7 for various values of K_eq and [total a]/[total d]. The error of representation of K_eq by FRETN increases as [total a]/[total d] gets farther from 1. (The effect of [total a]/[total d] = x is the same as the effect of [total a]/[total d] = 1/x for any x.) The effect of [total a]/[total d] being farther from 1 becomes more pronounced as K_eq increases. Therefore the optimal sensitivity and reliability of the difference in FRETN as a measure of the difference in K_eq between experimental and control is achieved when experimental and control have [total a]/[total d] close to each other and close to 1. Table 8 contains the values of ()/( · T_a) for the data analyzed in this report where T_d and T_a are the percent transmissions of the neutral density filters in the Donor and Acceptor filter sets, respectively. ()/( · T_a) is proportional to [total a]/[total d] with a proportionality constant which is the same for experimental and control if no filters are changed in the filter sets, except for possibly the neutral density filters. Therefore, if the values of ()/( · T_a) for experimental and control are similar, then the values of [total a]/[total d] are also similar. No conclusion can be made as to whether the values of [total a]/[total d] are close to 1 without more information, namely the excitation intensity with each filter set and the excitation efficiencies of the donor and acceptor. In Table 8 the values of ()/( · T_a) (and therefore [total a]/[total d]) are indeed similar, increasing the confidence in the use of FRETN as a measure of K_eq. However, when the control has a low K_eq and the experimental has a high K_eq, as is the case of strong interaction versus weak or no interaction, then [total a]/[total d] may be quite different from 1 or quite different between experimental and control and still allow FRETN to correctly reflect the change in K_eq.

View this table: [in this window] [in a new window]   TABLE 8   ( · Td)/( · Ta) mean and SD for the data in this report

One puzzling finding that emerged from this study was that the p values in Table 4 become smaller when going from the condition where no normalization with respect to donor and/or acceptor concentration is performed compared to the condition where normalization for just the donor concentration is performed, versus the situation where the p values increase when going from the condition where normalization with respect to donor concentration is performed compared to normalization of both the donor and acceptor concentration. The purpose of normalization is to compensate for variability in the concentrations of the reactants. However, if the measurement error of the concentration exceeds the reduction in error expected after normalization, then normalization may actually increase the variability. It appears that normalizing the calculation of FRET for the donor concentration results in near-optimal measurement of FRET and subsequent normalization by the acceptor concentration increases the variability in the resulting FRETN value. This suggests that there is a correlation between the concentrations of donor and acceptor such that normalizing by both (with the present level of measurement error) does not improve the result. A corollary of this is that in such a case the method using two-filters sets and assuming that the acceptor concentration is a constant times the donor concentration, FRET4/, would be expected to have p values as small or smaller than FRETN. This expectation is realized in Tables 4 and 6 where in the presumed interacting case the donor and acceptor concentrations are correlated (correlation coefficients 0.61 and 0.95, respectively). Table 6 uses the same data as in Table 4 except that two of the presumed interacting specimens have been omitted. The omitted specimens were outliers and their omission caused the correlation coefficient of the donor and acceptor concentrations to increase from 0.61 to 0.95. In Table 4, where there is lower correlation, FRET4/ has the same p value as FRETN, but in Table 6, where there is higher correlation, FRET4/ has a lower p value than FRETN. It is also possible to pose this argument in reverse: good performance of the methods using two-filter sets suggests that the donor and acceptor concentrations are correlated. In the data from Tables 4 and 5, and have correlation coefficients of 0.61, 0.45, and 0.57 for Beclin with Bcl-2, mutant Beclin with Bcl-2, and Bcl-2 with SERCA, respectively. In situations where the donor and acceptor concentrations were less well correlated or not correlated at all, the p values would be smaller when normalization for both donor and acceptor is performed. Therefore it is worth considering whether a method using only two-filter sets and normalizing for only one concentration will detect the purported interaction in a given experimental system. A significant increase in FRET obtained using the two-filter set method may be due either to an increase in the equilibrium constant for interaction (true positive) or to a systematic difference between the experimental and the negative control in the concentration of donor or acceptor or both (false positive). If an argument can be made that such a false positive is improbable, then the result can be accepted. Demonstration of the lack of systematic difference between the experimental and the negative control with regard to the concentrations of donor and acceptor can be made via the three-filter set method generating FRETN, , and . However, this is just what the use of the two-filter set method is trying to avoid. The validity of the two-filter set method could be verified by performing three-filter set measurements initially, and subsequently the two-fil