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Photobleaching-Corrected FRET Efficiency Imaging of Live Cells

Department of Immunology, The Scripps Research Institute, La Jolla, California

Correspondence: Address reprint requests to Tomasz Zal, Dept. of Immunology, The Scripps Research Institute, 10550 North Torrey Pines Rd., La Jolla, CA 92037. Tel.: 858-784-8184; E-mail: tzal{at}scripps.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX: GLOSSARY ACKNOWLEDGEMENTS REFERENCES

 
Fluorescent resonance energy transfer (FRET) imaging techniques can be used to visualize protein-protein interactions in real-time with subcellular resolution. Imaging of sensitized fluorescence of the acceptor, elicited during excitation of the donor, is becoming the most popular method for live FRET (3-cube imaging) because it is fast, nondestructive, and applicable to existing widefield or confocal microscopes. Most sensitized emission-based FRET indices respond nonlinearly to changes in the degree of molecular interaction and depend on the optical parameters of the imaging system. This makes it difficult to evaluate and compare FRET imaging data between laboratories. Furthermore, photobleaching poses a problem for FRET imaging in timelapse experiments and three-dimensional reconstructions. We present a 3-cube FRET imaging method, E-FRET, which overcomes both of these obstacles. E-FRET bridges the gap between the donor recovery after acceptor photobleaching technique (which allows absolute measurements of FRET efficiency, E, but is not suitable for living cells), and the sensitized-emission FRET indices (which reflect FRET in living cells but lack the quantitation and clarity of E). With E-FRET, we visualize FRET in terms of true FRET efficiency images (E), which correlate linearly with the degree of donor interaction. We have defined procedures to incorporate photobleaching correction into E-FRET imaging. We demonstrate the benefits of E-FRET with photobleaching correction for timelapse and three-dimensional imaging of protein-protein interactions in the immunological synapse in living T-cells.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX: GLOSSARY ACKNOWLEDGEMENTS REFERENCES

 
Recent development of variants of the green fluorescent protein has provided genetically encoded tags for specific fluorescent labeling of proteins. This has spurred great interest in the development of fluorescence resonance energy transfer (FRET) imaging techniques to visualize protein interactions in living cells with subcellular resolution (Mitra et al., 1996; Heim and Tsien, 1996). FRET is a short-range (<10 nm) effect whereby excitation of the donor fluorophore is transferred to the acceptor. When the donor and acceptor are attached to macromolecules, FRET shows that the molecules are in close apposition, presumably interacting. FRET results in several characteristic changes in local sample fluorescence, which can be spatially resolved in the form of FRET images. Firstly, fluorescence of donor is quenched. This can be measured by the recovery of donor fluorescence after photobleaching of the acceptor (donor dequenching; Szaba et al., 1992; Bastiaens and Jovin, 1996). Secondly, fluorescence of the acceptor (if it is a fluorophore) is induced upon donor excitation. This is the basis of sensitized emission imaging methods (Uster and Pagano, 1986). Thirdly, the lifetime and polarization of donor fluorescence are modulated by FRET. These can be resolved by fluorescence lifetime imaging microscopy (FLIM; Bastiaens and Squire, 1999; Kusumi et al., 1991).

The goal of FRET imaging is to visualize and quantitate molecular interactions in biologically relevant terms. Such measurements should be independent of the local concentrations of donor and acceptor molecules. Donor dequenching measurements are the most straightforward in that they report FRET directly in terms of well-defined FRET efficiency values (E). The other methods monitor FRET in the form of user-defined FRET indices. Unfortunately, irreversible destruction of acceptor makes the donor-dequenching method incompatible with timelapse imaging in living cells. FLIM has been successfully implemented for live cell studies, although it requires highly specialized instrumentation and expertise.

Sensitized-emission imaging is becoming the most popular approach to nondestructive, live FRET imaging, as it can be implemented on widefield and confocal microscopes. Thus, the sensitized fluorescence of acceptor is detected through an optical FRET filter set selecting acceptor emission during donor excitation (I_DA image). In practice, the I_DA image is contaminated by directly excited fluorescence of acceptor and by the tail of the donor emission spectrum. To account for this bleedthrough or crosstalk and to render the FRET index independent of fluorescence intensity, two additional images are acquired: acceptor fluorescence during acceptor excitation (I_AA) and donor fluorescence during donor excitation (I_DD). Given that the crosstalk coefficients of acceptor and donor in the FRET filter set, a and d, respectively, are constant and assuming that no other crosstalk components are present, sensitized emission, F_c, can be calculated by linear unmixing of the I_DA intensity (Tron et al., 1984; Youvan et al., 1997; Gordon et al., 1998).

(1)

F_c per se is still dependent on fluorophore concentration, which has led over the years to the implementation of many ratiometric FRET indices.

The typical makeup of an index used to detect FRET from the sensitized emission is a ratio designed such that its value should increase with FRET. The numerator of the ratio contains the I_DA intensity and modifications to correct for crosstalk. The particulars of crosstalk correction constitute one source of differences between FRET indices. The denominator is even more contentious since it not only provides for a way to render the whole index independent of fluorescence intensity, but also defines the correlation of the FRET index in terms of the particular parameters of the experiment. Therefore, the various published FRET indices can be grouped according to which fluorescence—donor (group 1), acceptor (group 2), or both (group 3)—denominate the FRET index. This way of classification of FRET indices is helpful because it reduces the superficial abundance of FRET indices to several representatives (Table 1 and Methods).

Repeated imaging of fluorescence is almost invariably accompanied by gradual photobleaching of fluorophores. This inadvertent photobleaching is usually slow, unlike the intentional acceptor photobleaching for the donor-dequenching method, but nevertheless it gradually affects the correspondence between the fluorescence intensity of donor and/or acceptor and the concentrations of the corresponding carrier molecules X and Y. If photobleaching occurs, a decrease in any FRET index published to date does not necessarily indicate the dissociation of the XY complex.

The fundamental, instrument-independent measure of FRET is the FRET efficiency, E. This is defined as the proportion of the excited states of the donor that become transferred to the acceptor. Measurements of E for samples undergoing dynamic interactions result in the apparent FRET efficiency, E_app, which is the product of the specific efficiency of the complex, E_max (if only one species is formed), and _D, the degree of donor-acceptor complex [DA] formation with respect to fluorescent donor [D_total].

(2)

Thus, E_app is biologically relevant because it is proportional to the degree of complex formation with respect to the donor-labeled molecule X (but only if the sample is not subject to photobleaching during the experiment). E_max is typically determined in vitro from samples of donor and acceptor that are complexed homogenously, stoichiometrically, and completely with each other. If E_max is known, the spatiotemporal distribution of _D in subcellular compartments can be explicitly determined from FRET images, if these are obtained in terms of E_app.

In this study, we describe a nondestructive, 3-cube method, termed E-FRET, to measure E_app on a pixel-by-pixel basis. This is possible thanks to a novel way of calibrating the imaging system for the relationship between E and sensitized emission. Furthermore, we demonstrate practical computational approaches to correct E_app for photobleaching, both in timelapse and three-dimensional experiments. This is done by calculating E_corr, which is the FRET efficiency that would be apparent if there was no photobleaching. This extends the time frame of live FRET imaging, improves quantitation of the FRET data, and facilitates their interpretation in terms of the degree of molecular interaction with respect to the donor-labeled molecules.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX: GLOSSARY ACKNOWLEDGEMENTS REFERENCES

 
DNA constructs and cells
We divide FRET constructs into three classes, depending on how well donor and acceptor concentrations correlate throughout the cell. In Type 1 experiments, donor and acceptor are attached to the same carrier molecule so that their concentrations are correlated. Such constructs are used to detect conformational changes that increase or reduce the FRET signal. In Type 2 experiments, donor and acceptor are joined by a linker that can be enzymatically digested. Donor and acceptor concentrations are correlated before the linker is digested, but may distribute differently in the cell thereafter; for example, if the FRET construct is targeted to cell membranes. In such cases, Type 2 experiments require full crosstalk correction typical of Type 3 experiments; otherwise they can be treated as Type 1. Type 3, or intermolecular FRET, is the most general category, whereby donor and acceptor are attached to different macromolecules; hence their concentrations are not correlated.

Type 1 constructs CFP-lck-YFP and YFP-CFP were designed to undergo constitutive energy transfer with low and high efficiency, respectively. CFP and YFP-Q69K (Miyawaki et al., 1999) cDNA (from pECFP-N1 and in-house mutated pEYFP-N1, Clontech, Palo Alto, CA) were inserted after the unique domain and at the end of mouse p56lck cDNA, respectively. EYFP and ECFP were joined by a 10-amino-acid linker. The constructs were transfected into the A18 T-cell hybridoma (Zal et al., 2002). The FRET efficiency for CFP-lck-YFP was E = 10% and for YFP-CFP E = 33%, as determined from donor recovery after acceptor photobleaching. E was independent of the level of expression, the activation state of the cells, or intracellular compartmentalization. For Type 3 experiments we used the A18.ZC.4Y cells coexpressing the CD3-CFP and CD4-YFP fusion proteins or CD4-CFP and CD4-YFP. Formation of intercellular contacts was induced by mixing A18.ZC.4Y cells with C5-peptide-loaded LK35 B cell tumor as described before (Zal et al., 2002). The CD4-CFP and CD4-YFP pair was cotransfected in the CD4-negative A18 cells by nucleoporation (Amaxa Biosystems, Cologne, Germany). After 24 h, CD4 was cross-linked by the GK1.5-biotin antibody (Southern Biology Associates, Birmingham, AL) and streptavidin-allophycocyanin (Molecular Probes, Eugene, OR). FRET was measured in the areas of clustering identified by the allophycocyanin fluorescence. Autofluorescence could be almost eliminated in lymphocytes by growing cells overnight in the riboflavin-low, HEPES-buffered 199 medium with Hanks salts (GIBCO, Invitrogen, Carlsbad, CA), supplemented with 5% FCS, 50 µM ß-mercaptoethanol, 2 mM L-glutamine, and without antibiotics.

Microscopy
Two widefield microscope systems were used for this work. The DeltaVision system consisted of an Olympus IX70 (Olympus, Melville, NY) microscope equipped with a 100-W mercury lamp, Photometrics CH350L (Roper, Tucson, AZ) cooled charge-coupled device (CCD) camera, and the SoftWorx 2.0 acquisition and analysis software (Applied Precision Instruments, Issaquah, WA). The optical filters (Chroma, Rockingham, VT) were 436/10 nm, 470/30 nm (CFP excitation and emission) and 500/20 nm, 535/30 nm (YFP excitation and emission). The JP4 multi-bandpass dichroic mirror was stationary. Different combinations of excitation and emission filters were introduced into the light-path of the microscope by filter wheels.

The second microscope system was specifically designed for fast FRET imaging to reduce errors due to cellular motility. This system was based on simultaneous acquisition of donor emission and acceptor emission during donor excitation by two CoolSnapHQ cameras (Roper, Tucson, AZ) attached to a Zeiss 200-M microscope through a beamsplitter (custom 510LPXR, Chroma, Rockingham, VT) and stationary emission filters. Rapid wavelength switching between donor and acceptor excitation was performed with a DG4 galvo illuminator customized with a 300W xenon lamp (Sutter, Novato, CA). YFP excitation for sensitized-emission imaging was attenuated to 20% by appropriate positioning of the exit mirror and was left at 100% for donor recovery measurements. The system was managed by Slidebook software (3I Corporation, Denver, CO). The optical filters were 430/25 nm, 470/30 nm (CFP excitation and emission) and 510/20 nm, 550/50 nm (YFP excitation and emission), and the JP4 dichroic mirror. Cameras were typically run in 2 x 2 binning mode with software flatfield correction and estimated noise of <2%. Images were automatically aligned with subpixel resolution through the frequency-based algorithm of the Slidebook software. Background was removed based on the average reading in a cell-devoid area of each image.

Crosstalk calibration
Crosstalk or bleedthrough of fluorescence between the donor and acceptor's emission spectra must be removed or rendered constant for specific detection of the FRET signal. The principle of crosstalk removal through the linear spectral unmixing algorithm (Gordon et al., 1998; Youvan et al., 1997) is valid for fluorophores which do not exhibit changes of the emission spectrum due to environmental factors other than FRET. In particular, the intensity of each crosstalk component remains in constant proportion to the main fluorescence of each fluorophore. Crosstalk coefficients are calculated by the image math, i.e., on a pixel-by-pixel basis. Cells expressing a range of levels of donor or acceptor are used to verify that crosstalk coefficients are indeed constant across the range of concentrations and subcellular compartmentalization. Thus, acceptor-only and donor-only cells are imaged using the donor excitation-donor emission (I_DD), donor excitation-acceptor emission (I_DA), and acceptor excitation-acceptor emission (I_AA) filter combinations. Coefficients a and b for acceptor bleedthrough in the I_DA and I_DD filter sets and c and d for donor bleedthrough in the I_AA and I_DA filter sets, respectively, are defined below.

(3)

(4)

(5)

(6)

I represents the pixel-by-pixel image intensity, minus background, using the combination of excitation and emission filters indicated by the lower index, for samples containing only donor or acceptor, as indicated in parentheses. Finally, if the crosstalk coefficients are constant across cells in the field of view, their averages are calculated from several areas encompassing single cells. This cancels high frequency noise and increases precision. Bleedthrough parameters for ECFP and EYFP on the DeltaVision system were a = 0.21 ± 0.01, d = 0.95 ± 0.05, b = c = 0. For the dual-camera 3I system, a = 0.0154 ± 0.0011 (a = 0.077 at 20% YFP excitation), d = 0.647 ± 0.023, and b = c = 0. The difference between the microscopes in the a-coefficient was mostly due to the mercury vs. xenon illumination, whereas d was lower in the dual-camera system thanks to the optimized filters and the beamsplitter between cameras.

Bleedthrough coefficients were constant for ECFP and EYFP within living cells, as demonstrated previously (Zal et al., 2002). If the crosstalk coefficients do not appear constant, possible causes of crosstalk calibration errors have to be considered. These include cell autofluorescence, the lack of flatfield correction, and incorrect background subtraction, as well as detector nonlinearity and/or low dynamic range of signal digitization.

Existing methods
Group 1 FRET indices (donor-denominated) have been formulated as the F_c/D ratio of the I_DA intensity, with both donor and acceptor bleedthrough subtracted, to the donor fluorescence (Kam et al., 1995, Gordon et al., 1998). Alternatively, only the acceptor bleedthrough is subtracted from I_DA and ratioed to the donor image, rendering the donor bleedthrough constant (F_a/D) (Zal et al., 2002). Group 2 indices (acceptor-denominated) are exemplified by the F_c/A ratio of the crosstalk-subtracted I_DA image to the acceptor image (Jiang and Sorkin, 2002). This is similar to the FR ratio for effective FRET efficiency (Erickson et al., 2001). Group 3 indices are donor- and acceptor-denominated. At a high local concentration of donor and acceptor, FRET can be caused by diffusion-driven random collision (Gordon et al., 1998). To compensate for this effect, these workers proposed using the ratio of sensitized emission to the product of donor and acceptor fluorescence (FRETN). Another group 3 formula, the ratio of the sensitized fluorescence to the square-root of the product of donor fluorescence and acceptor fluorescence, was put forward recently (N_FRET; Xia and Liu, 2001).

Basic E-FRET formulae
Our first goal was to standardize FRET imaging by calculating E from the 3-cube intensities I_DA, I_DD, and I_AA. This would allow us to replace arbitrary, instrument-dependent FRET indices with E, and thus to relate 3-cube FRET imaging to donor recovery after acceptor photobleaching or FLIM measurements. The apparent FRET efficiency of a sample, E_app, is given by the relative increase of donor fluorescence after complete acceptor photobleaching, which is the basis for the donor-dequenching method,

(7)

To calculate E_app from the I_DA, I_DD, and I_AA intensities, we define the parameter G as the ratio of the sensitized emission F_c to the corresponding amount of donor recovery in the I_DD channel after acceptor photobleaching,

(8)

is the intensity of donor fluorescence after acceptor photobleaching. G is similar to the parameter defined theoretically before (Gordon et al., 1998). The proof that G as defined by Eq. 8 is constant, and the method to determine G experimentally, is provided in the following section. Combining Eqs. 7 and 8 allows us to eliminate :

(9)

The sensitized fluorescence F_c is calculated by subtraction of the major crosstalk components from I_DA and the minor crosstalk components from I_DD and I_AA, using previously calibrated crosstalk coefficients a, b, c, and d, defined in Eqs. 3–6:

(10)

If the minor crosstalk components are negligible, b = c = 0, F_c is given by the more familiar Eq. 1. Introducing F_c from Eq. 10 or Eq. 1 (for b = c = 0) we arrive at the general E-FRET formulae, which allow calculation of E_app from terms measured by 3-cube imaging:

(11)

(12)

FRET data from 3-cube imaging are frequently visualized in terms of the F_c/I_DD ratio. A form of the E-FRET formula, which is useful for calculating E_app from the F_c/I_DD ratio, is given as

(13)

where R = F_c/I_DD (Table 1). The E-FRET formula Eq. 11, Eq. 12, or Eq. 13 is applied on a pixel-by-pixel basis through image math. The result is an image with pixel values between 0 and 1, which is programmed in the software to be presented in a color-encoded scale.

Determination of the G parameter
The parameter G is crucial to calculation of FRET efficiency because it relates the level of sensitized emission to the drop in donor fluorescence attributable to FRET. To prove that G, as defined in Eq. 8, is a constant parameter for a given imaging system and fluorophores, we consider the following. The intensity of sensitized emission F_c is proportional to the concentration of the donor-acceptor complex [DA], the intensity of illumination reaching the sample through the donor excitation filter _D, the absorption coefficient of donor _D, the specific FRET efficiency of the complex E_max, the quantum yield of acceptor Q_A, the throughput of the acceptor emission light-path L_A, the quantum sensitivity of the camera for acceptor emission S_A, and the exposure time for the I_DA image t_DA. The amount of donor fluorescence recovery after acceptor photobleaching is proportional to [DA], _D, _D, E_max, the quantum yield of donor Q_D, the throughput of the emission light-path including the donor emission filter L_D, the quantum sensitivity of the camera for donor emission S_D, and the exposure time for the I_DD image, t_DD. The value _D is the same for imaging through the I_DD and I_DA filter sets, when using a fixed multi-bandpass dichroic beamsplitter and no neutral density filters. Therefore

(14)

As evident from Eq. 14, G is constant for a given choice of fluorophores (Q_D and Q_A) and the imaging setup (L_D, L_A, S_D, and S_A) and independent of underlying FRET efficiency, essentially as described before (Gordon et al., 1998). Thus, G can be calibrated using a reference FRET sample with a different E_max than in the experiment as long as exposure timings remain proportional and the same donor and acceptor fluorophores are used.

A relatively simple and direct way to measure G merges donor recovery after acceptor photobleaching with sensitized-emission imaging. Cells expressing the constitutive FRET constructs CFP-lck-YFP or YFP-CFP are fixed and imaged using all three filter combinations to record the I_DD, I_DA, and I_AA images. Then the acceptor is photobleached by extended illumination through the acceptor excitation filter. Photobleaching destroys fluorophores asymptotically, hence incompletely. Therefore cells are imaged again using all three filter set combinations to capture the and images. Substituting F_c in Eq. 8 and allowing for the incomplete photobleaching of acceptor gives the formula for experimental determination of G:

(15)

To increase precision, average fluorescence intensities of user-drawn regions-of-interest (ROI) are used. We used whole cells, for which the particular ROI shape is not critical. For ECFP and EYFP on the DeltaVision system, we measured G = 5.1 ± 0.15 and for the dual-camera 3I system G = 3.5 ± 0.1.

Methods for correction of E for photobleaching
Our second goal was to introduce correction for photobleaching, which degrades measurements in timelapse and three-dimensional experiments. The main problems to consider are: 1), the different photosensitivities of donor and acceptor; 2), the effect of sensitized photobleaching (Mekler et al., 1997); and 3), changes in cell morphology and/or focal position. Depending on the setup of the imaging experiment we will define internal and external correction for photobleaching.

E_corr: photobleaching-corrected FRET efficiency
Photobleaching breaks the correspondence between fluorescence intensity of the fluorophore and the concentration of carrier molecules X and Y. Thus, the degree of fluorescent complex formation with respect to total donor _D = [DA]/[D_total] is no longer equivalent to the degree of complex formation with respect to the donor-carrying molecule X: [XY]/[X_total]. ([DA] [XY] are the concentrations of fluorescent XY complexes and all XY complexes, respectively, and [D_total] [X_total] are the total concentrations of fluorescent X molecules and all X molecules, respectively.) To introduce imaging-induced photobleaching into the E-FRET formula we will define E_corr, which would be apparent if there was no photobleaching, i.e., with respect to the carrier molecule X:

(16)

The distinction E_corr in Eq. 16 and E_app in Eq. 2 is that the latter refers to the fluorescent tags, which are affected by photobleaching, whereas the former refers to the carrier molecules themselves, which are the true interest of the biologist. Given stoichiometric and complete labeling of carrier X by donor and carrier Y by acceptor, and no prior exposure of the sample to photobleaching, the starting conditions are and .

Internal correction
One of the derivative effects of FRET is the accelerated bleaching of acceptor and decreased bleaching of donor in the sites of interaction. Sensitized photobleaching of acceptor is caused by the energy transferred from the donor during donor excitation. On the other hand, the energy transfer decreases the lifetime of the donor's excited state, hence the rate of donor photobleaching. Due to these effects, donor and acceptor are photobleached with spatially and temporally variable rates and , respectively. The rate coefficients and are dependent on the local E_app and on the rate of exchange of the carrier molecules between the areas of low and high interactions. If there is a fast equilibrium between free and complexed X and Y, i.e., if the half-life of the complex is shorter than the imaging interval, diffusional mixing will ensure uniform photobleaching within the topologically enclosed compartment. This compartment can be the whole cell or an intracellular structure. In such cases, mathematically accurate photobleaching correction is straightforward. Approximate correction is possible in the remaining situations.

Let us first consider an experimental setup where photobleaching due to imaging is slower than the rates of complex formation and dissociation. Due to equilibration by diffusion, the photobleaching rate coefficients (t) and (t) will fluctuate with time, depending on the average E_app. Total fluorescent donor at time t is given by , and total fluorescent acceptor is . At equilibrium, the fraction of DA complexes in which both donor and acceptor are still fluorescent at time t is given by . Therefore . Introducing these terms into Eq. 16 and noting E_app in Eq. 2, we arrive at the formula describing correction of E_app for photobleaching:

(17)

It is apparent that deviation of E_app from E_corr in experiments where donor-acceptor interaction kinetics are faster than the rates of photobleaching is caused only by acceptor photobleaching. Thus, E_corr is calculated for each time point by multiplying the apparent FRET efficiency E_app, given by Eq. 11, Eq. 12, or Eq. 13, by the ratio of the total acceptor fluorescence at the beginning of imaging, to the total acceptor fluorescence at time t, (both corrected for crosstalk if c > 0). The readings are taken over whole cells or ROIs corresponding to subcellular compartments within which FRET is measured, as

(18)

Simplified correction is possible if acceptor photobleaching adheres to first-order kinetics (i.e., is time-independent) and the minor bleedthrough coefficient c is zero:

(19)

In this case, photobleaching correction is based on the acceptor half-life, _A. Acceptor half-life is derived from fitting the exponential curve I_AA 2^–t/ to the total I_AA intensity in a cell or subcellular compartment, using the time course of acceptor images. Time t is the running total illumination time and can be expressed in terms of the time point number instead. Eq. 19 is less sensitive to random fluctuations than Eq. 18 thanks to the interpolation and should be used for experiments where acceptor photobleaching can be approximated with a single exponential. Appropriate image math operations to implement calculation of E_corr according to Eq. 18 or Eq. 19 were programmed into the image processing software (3I Corporation) utilizing the direct-fit or exponential-fit photobleaching correction algorithms, respectively.

Approximated correction for slow interactions
Approximated correction will typically be required where the frequency of image capture is greater than the half-life of the complex or if diffusion is restricted. Acceptor photobleaching will be faster in the areas of increased E_app due to insufficiently fast exchange with the pool of free fluorophores. Nevertheless, if the overall FRET efficiency is low, then most of the acceptor loss can be attributed to direct excitation with the I_AA filter set, rather than to FRET sensitization (see below). Donor will photodestruct slower in sites of complex formation, but this effect is largely cancelled for low E_app by the ratiometric nature of E, Eq. 17. Therefore, good photobleaching correction is possible based on the total instead of a strictly local rate of acceptor photobleaching.

Next, we estimate the maximum error incurred with such correction and ask how deeply acceptor can be photobleached for the desired precision, set at 10% of E_corr. Let _free be the rate of acceptor photobleaching due only to direct illumination of acceptor, i.e., in areas of noninteraction, or in a sample containing acceptor alone. The value _free sets the limit of error for the true rate of acceptor photobleaching in areas of interaction. The rate of direct acceptor photobleaching caused by illumination with wavelengths ₁ and ₂, used for donor and acceptor excitation, depends on the respective illumination intensities ₁ and ₂, the length of exposures t₁, t₂, and the absorbance coefficients of acceptor _A1, _A2 at ₁ and ₂. The rate of sensitized acceptor photobleaching is proportional to _1D1t₁E_maxA, where _D1 is the absorbance coefficient of donor at the donor excitation wavelength, and _A = [DA]/[A]_total is the local degree of complex formation with respect to acceptor. Thus, the local rate of acceptor photobleaching in an interacting sample is

(20)

Therefore, the limit of error caused by using _free instead of for photobleaching correction is

(21)

where _A,free is the half-life of free acceptor in the control sample. Let us assume continuous interaction with maximum acceptor occupancy _A = 1 and E_max = 25%. For our imaging system, the timing t₁ = t₂ and the intensity of exposures _{1 2}, when using similar bandwidth for excitation, no neutral filtering, and a xenon source. For CFP and YFP, _D1 = 26,000 M^–1 cm^–1, _A1 = 2520 M^–1 cm^–1, and _A2 = 65,520 M^–1 cm^–1 (₁ = 430/25 nm, ₂ = 510/20 nm), hence m 0.38. Thus the error of correction will remain <10% of E_corr until >67% of acceptor is photobleached (1.6_A,free).

A more general estimate is possible for imaging systems using different light sources and/or filters. Typically, imaging of FRET is set up such that intensities of images remain within the same order of magnitude. Thus, _1D1t₁Q_D = _2A2t₂Q_A. Therefore, for fluorophores with quantum yields of similar magnitude, m 1. In the worst case scenario of m = 1, photobleaching correction is possible, with accuracy >10% of E_corr, until up to 35% of the acceptor is destroyed. In practice, correction is calculated using the average rate of acceptor photobleaching in the sample or cell compartment according to Eq. 18 or Eq. 19, which will introduce significantly less error.

External correction
Experiments involving changing focal planes (three-dimensional, four-dimensional) or extensive cell movement are not amenable to the internal correction because the overall acceptor intensity does not reflect the progress of acceptor photobleaching. In such cases external correction is applied using the half-life of acceptor in a reference sample subjected to the same sequence of exposures as intended for the experiment. The reference sample may be noninteracting or acceptor-only but closer approximation is obtained from a sample with E_app matching the basal E_app during the experiment. The value _A in the reference sample is applied to the experimental data according to Eq. 19. If the rate of acceptor photobleaching does not adhere to the simple exponential model, the external compensation multipliers (assuming c = 0) are determined for each time point using the reference sample and applied according to Eq. 18 for corresponding time points of the experiment. The distinct benefit of external compensation is such that the acceptor half-life _A or the compensation multipliers can be measured using short timelapse intervals and can then be applied to experimental data with longer timelapse intervals and/or changing focal planes (but not the x–y coordinates). The maximum error due to sensitized photobleaching, and the limit of allowable acceptor photobleaching for external correction are the same as estimated above for stable interactions. It is important to note that any error due to the rate of acceptor photobleaching determined in a noninteracting sample instead of the actual rate in experiment results only in undercorrection and will not cause false-positives.

Mathematical modeling
Mathematical simulation of the responses of FRET indices (listed in Existing Methods, above) and the basic E-FRET formula Eq. 12 to varying concentration of donor and acceptor was performed to establish how well they correlate with the degrees of interaction. First, we derived general equations linking each FRET index to the degree of interaction with respect to donor _D = [DA]/[D_total], or to the degree of interaction with respect to acceptor _A = [DA]/[A_total]. [DA] is the concentration of donor-acceptor complex, and [D_total], [A_total] are the total concentrations of donor and acceptor, respectively. Derivation of equations for the simulation is described in the Appendix and collected in Table 1. The equations were programmed into a spreadsheet software program (Excel 2000, Microsoft, Redmond, WA). Graphs of the responses by each formula were generated by varying the concentration of donor, acceptor, or both, assuming a high affinity interaction and no photobleaching. Concentrations were normalized to facilitate comparison of trends. For modeling purposes we set parameters typical for CFP and YFP with mercury illumination: the crosstalk of donor and acceptor fluorescence into the FRET filter set are d = 0.9 and a = 0.25, respectively, the detection sensitivity per mol for the I_AA filter set being R_AA = 1.5 R_DD of the sensitivity of the I_DD filter set, and the ratio of sensitized emission to the decrease of the donor fluorescence G = 4. The specific FRET efficiency of the complex was set at E_max = 40%. Parameters E_max, G, a, and d are instrument- and fluorophore-specific and different values of these parameters affect scaling but do not change the trends and general relationships between curves.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX: GLOSSARY ACKNOWLEDGEMENTS REFERENCES

 
To illustrate the benefits of the E-FRET method for imaging of molecular interactions in living cells, it is important to use it both for internal FRET constructs as well as for interactions between independent molecules. We distinguish three types of FRET experiments with respect to the degree of fluorophore correlation. Type 1 experiments encompass constructs where donor and acceptor are attached to the same carrier, such that FRET efficiency is modulated by conformational changes. This ensures correlation between the fluorophores and normally warrants simplified, 2-cube FRET imaging (except when photobleaching is encountered). Type 2 constructs incorporate a digestible linker between the fluorophores. The suitability of 2-cube imaging for Type 2 constructs depends on subcellular compartmentalization of donor and acceptor after their separation by the proteolytic activity. Lastly, Type 3 experiments are the most general, and, arguably, the most interesting category, where donor and acceptor are on different carrier molecules. Their concentrations are not correlated, which necessitates explicit crosstalk correction, hence 3-cube imaging. Here, we use the interaction between the CD3-CFP chain of T-cell receptor and CD4-YFP co-receptor during the recognition of antigenic peptide-MHC-II complexes by T-lymphocytes. Quantitative monitoring of the interaction in timelapse and three-dimensions is important to understand the function of the immunological synapse formed between T-cells and antigen-presenting cells (Gascoigne and Zal, 2004; Zal et al., 2002). First, we show that combination of two FRET methods: sensitized-emission imaging and the donor recovery after acceptor photobleaching allows us to measure the G parameter, which is crucial for E-FRET calculations. We show that G is constant for a given imaging system and that it can be calibrated using a reference FRET construct, as described in Methods. Subsequently, we show that E-values obtained by the E-FRET method are equivalent to E measured by the donor-dequenching technique. We then demonstrate the advantage of E-FRET with photobleaching correction for timelapse and three-dimensional imaging of antigen recognition by T-lymphocytes. Lastly, we compare the E-FRET method to existing FRET indices for their ability to correlate with the degree of molecular interaction.

Calibration of the G-factor and calculation of E
Calculation of FRET efficiency (E) from 3-cube imaging data requires knowledge of the correlation factor G between the sensitized emission and the concomitant drop in donor fluorescence. G should be constant for a given choice of donor, acceptor, and imaging parameters, and independent of E_app, as shown on theoretical grounds by Gordon and co-workers (1998) and here by Eq. 14. To verify experimentally that G is constant for our imaging system, we photobleached YFP in cells expressing varying levels of the YFP-CFP construct and visualized G on a pixel-by-pixel basis. The average G was indeed constant for different concentrations of YFP-CFP (exemplified by two cells in Fig. 1, A and B), whereas some pixel-to-pixel variation could be attributed to the camera noise and specimen stability during the time required for photobleaching. Next, we plotted the absolute values of the change in sensitized emission versus the absolute values of the increase of donor fluorescence after partial (50–60%) and complete (95%) photobleaching (Fig. 1 C). These were co-linear, demonstrating the validity of Eq. 15, with the slope G = 3.50 (for ECFP, EYFP on the dual-camera microscope, see Methods).

View larger version (22K): [in this window] [in a new window]   FIGURE 1  Calibration of G and validation of E-FRET calculation. The G factor was determined on a pixel-by-pixel basis using cells expressing varying levels of the YFP-CFP construct. (A) Two cells are shown with a twofold difference in fluorescence intensity (YFP channel). (B) The same area shown in terms of the G factor calculated by Eq. 15 after photobleaching of YFP by 3-min illumination (95% decrease in YFP intensity). The average value for the upper cell was G = 3.42 and for the lower cell G = 3.47. Standard deviations were SD = 0.15 and SD = 0.13, respectively. (C) G determined from the slope of the correlation between the drop in sensitized emission and CFP recovery, after complete and partial photobleaching of YFP in the YFP-CFP construct. (D) The apparent FRET efficiency Eapp was determined by the donor-recovery method for cells expressing YFP-CFP (open diamonds) and for cross-linking of CD4 in cells coexpressing CD4-CFP and CD4-YFP (shaded circles). The solid line represents the results of the E-FRET calculation using the values of the Fc/D index recorded before acceptor photobleaching and G = 3.50, demonstrating good agreement of the E-FRET method with the donor-recovery method for independent experiments. Dashed lines are for G = 2.5 (upper line) and G = 4.5 (lower line).

Imaging-induced photobleaching affects FRET measurements
Imaging-induced photobleaching is detrimental to prolonged FRET experiments. We therefore considered how photobleaching of donor and acceptor affect the apparent FRET efficiency E_app, and incorporated appropriate correction procedures. This allowed us to calculate the corrected FRET efficiency E_corr, which would be apparent if the sample was not photobleached (see Methods, Eq. 18 or Eq. 19). To evaluate the performance of photobleaching compensation under experimental conditions, we set up timelapse imaging of cells expressing the Type 1 fusion construct CFP-lck-YFP, which undergoes constitutive energy transfer with E_max = 10%. Fig. 2 A shows that prolonged imaging returned a decreasing E_app reading over time. Next, we introduced internal compensation according to Eq. 18 or Eq. 19. Both resulted in stable values of E_corr, as expected for a constitutive FRET construct (Fig. 2 A). Closer inspection of the data demonstrates that the E_corr values calculated by Eq. 19 are consistently slightly higher than E_corr calculated by Eq. 18. This is because Eq. 19 corrects up to E_corr as if no exposures of the sample were yet taken, whereas Eq. 18 corrects up to the amount of acceptor after the first exposure. Normally, the difference should be small and not significant, although Eq. 19 is advantageous for single exponential photobleaching.

View larger version (59K): [in this window] [in a new window]   FIGURE 2  Photobleaching correction during timelapse FRET imaging in Type 1 experiment. Cells expressing CFP-lck-YFP were imaged by taking 1 s exposures per time point to acquire the IDD, IDA, and IAA images. (A) Single-cell averaged image intensities, minus background, are shown in red (IDD, shaded squares; IDA, shaded triangles; and IAA, shaded circles). The value Eapp was calculated according to Eq. 12 (open circles). Photobleaching-corrected FRET efficiency Ecorr was calculated according to Eq. 19 (open squares), and using Eq. 18 (open triangles). Two experiments are demonstrated. (B) FRET efficiency imaging and photobleaching correction on pixel-by-pixel basis. Images of a cell from A are shown. The top row consists of images taken at the first time point: IDD (CFP), IAA (YFP), sensitized fluorescence (Fc, Eq. 1), the FRET ratios Fc/D and Fa/D, Eapp, and Ecorr using Eq. 19, defined in Table 1. The lower row shows corresponding images of the same cell at the time point n = 10.

Photobleaching compensation for Type 3 experiments
Type 3 experiments are the most general category of FRET experiments, whereby donor and acceptor are attached to separate macromolecules. Type 3 experiments introduce temporal variability of local E due to the dynamics of protein interactions within the cell, making it difficult to quantitatively demonstrate the effect of photobleaching correction independent of biological responses. To illustrate the benefits of FRET efficiency correction applied to timelapse and three-dimensional imaging of a Type 3 experiment, we used the interaction between the CD3 chain of T-cell receptor and CD4 co-receptor during antigen recognition in the immunological synapse of T-lymphocytes. Fig. 3 shows results of a timelapse experiment, where we imaged FRET between CFP attached to CD3 and YFP attached to CD4, both coexpressed in the A18.ZC.4Y T-cell hybrid (Zal et al., 2002). The A18.ZC.4Y cells were mixed with an excess of antigen-loaded antigen-presenting cells (LK35 B cell tumor) and allowed to form the intercellular contact areas, or immunological synapses. Both CD3-CFP and CD4-YFP were recruited to the synapses, and interacted as described before (Zal et al. 2002). We observed gradual loss of YFP fluorescence, Fig. 3 A, which was accompanied by decreasing E_app in regions of clustering of CD3 and CD4 in the cell membrane, Fig. 3 B. Internal correction was then applied based on the total whole-cell YFP signal and the first-order rate of acceptor photobleaching as per Eq. 19. As seen in Fig. 3 C, E_corr corrected for the loss of FRET due to the imaging-induced photobleaching. An increased pixel noise is evident in the E_corr image at n = 65 (Fig. 3 C) as compared with the time point n = 1. This is consistent with the general loss of fluorescence signal, hence a decreasing signal/noise ratio of the raw data (see the error propagation analysis below). The entire imaging sequence was analyzed for the average FRET efficiency in one contact area, selected with the white box in Fig. 3 A. The result is shown in Fig. 3 D. The overall trend of the average remained constant, despite the worsening signal/noise ratio.

View larger version (37K): [in this window] [in a new window]   FIGURE 3  Imaging of photobleaching-corrected FRET efficiency in Type 3 timelapse experiment. The A18.ZC.4Y cells expressing CD3-CFP and CD4-YFP were mixed with an excess of antigen-loaded antigen-presenting cells (LK35 B cell tumor), and allowed to form the intercellular contact areas for 30 min. Cells were then kept at room temperature to prevent gross changes in the cell shape during imaging. One-hundred-seventy-five time points were acquired and analyzed for FRET efficiency. The whole sequence took <3 min to acquire and we did not see any gross changes in the interaction between CD3 and CD4 at room temperature during this time. CFP (green) and YFP (red) fluorescence are shown merged after the first and 65th exposure cycle (A). Eapp calculated according to Eq. 12 (no photobleaching correction) is shown in B. Internal correction of Eapp was applied based on the total whole-cell YFP signal and first-order rate of acceptor photobleaching as per Eq. 19 (C). The lookup color table is below (E). The normalized total YFP fluorescence is shown in D, dark line (the starting whole-cell average YFP signal was 996.6 on a 12-bit scale), Eapp (shaded diamonds), and Ecorr (shaded squares).

View larger version (46K): [in this window] [in a new window]   FIGURE 4  E-FRET imaging with photobleaching correction in a three-dimensional FRET experiment. We acquired a series of 137 planes of a single contact area between the A18.ZC.4Y cell and antigen-loaded LK35 B cell, using the 100x NA 1.45 objective, timed as in Fig. 3. A and B show side (x–z) views of YFP and CFP fluorescence, respectively, in the contact area marked in E. C and D show, respectively, FRET efficiency between CD3-CFP and CD4-YFP without and with photobleaching correction.

Comparison with other ratiometric sensitized-emission methods
We used mathematical modeling under a variety of simulated experimental conditions to compare E_app calculated by the E-FRET formula with several representative FRET indices from each denominator group (defined in Methods and Table 1). We solved each of the formulae with respect to the degree of donor occupancy by acceptor _D or the degree of acceptor occupancy by donor _A (collected in Table 1 and explained in the Methods and Appendix). Responses were plotted along _D and _A over a range of donor and acceptor concentrations, such that any correlations or the lack of correlation with _D and/or _A could be recognized and demonstrated visually. The results of the analysis for both Type 1 experiments (donor and acceptor on the same molecule) and Type 3 experiments (donor and acceptor on different molecules) are summarized in Table 1. For brevity, we show only the simulation of a Type 3 experiment, where we reciprocally varied concentrations of donor and acceptor (Fig. 5). This simulation demonstrates that, regardless of the variable concentrations of donor and acceptor, group 1 indices F_c/D, F_a/D, as well as E_app, have the same trend as _D whereas group 2 indices F_c/A and F_d/A follow _A. In contrast, neither FRETN nor N_FRET (group 3) correlate consistently with either donor or acceptor occupancy throughout the whole range of their ratios. For example, increasing the acceptor concentration, while decreasing the donor concentration, causes FRETN to decline but _D remains constant. Likewise, increasing the donor concentration while decreasing acceptor concentration causes FRETN to decline, while _A stays constant. Additional simulations (not shown) demonstrate that FRETN correlates with _D only if the concentration of acceptor is constant and with _A only if donor concentration is constant. Similarly, N_FRET is concentration-dependent for Type 3 experiments, although less so than FRETN due to the square-root in the denominator of N_FRET. The only case when N_FRET retains correlation with _D (and _A) is in the special case of Type 1 experiments but in such a case the simpler F/D ratio is also suitable (not shown). F/D loses correlation with either degree of interaction for Type 3 experiments due to the incomplete crosstalk correction for acceptor (donor crosstalk is rendered constant by ratioing to the donor fluorescence).

View larger version (23K): [in this window] [in a new window]   FIGURE 5  Modeling of the responses of FRET methods to variable concentration of donor and acceptor attached to different carriers (Type 3 experiment). In this simulation, donor and acceptor concentrations change reciprocally (acceptor concentration increasing and donor concentration decreasing) and a high affinity interaction between the donor-labeled and the acceptor-labeled species is assumed. Responses of several representative FRET indices from each denominator group (nomenclature and formulae defined in Table 1) were calculated and plotted along the degree of donor interaction D (thin gray line, right y axis) and degree of acceptor interaction A (broken gray line, right y axis), such that any correlation could be recognized visually. The following indices were included for comparison with Eapp (solid black line, right y axis). Group 1, donor-denominated ratios: F/D (no crosstalk subtraction, x-marks), Fc/D (both donor and acceptor bleedthrough subtracted, ), Fa/D (only acceptor bleedthrough subtracted, •). Group 2, acceptor-denominated ratios: Fc/A (full crosstalk subtraction, ), Fd/A (only donor crosstalk subtracted, equivalent to FR x a (Erickson et al., 2001), ). Group 3, donor-acceptor denominated indices: FRETN (), and NFRET (). Nonratioed sensitized emission Fc is included for comparison (). Increasing the acceptor concentration while decreasing the donor concentration causes increasing D, up to D = 1 when donor and acceptor concentrations are equal ([D] = [A] = 0.5). When acceptor concentration exceeds donor concentration, donor is saturated and D = 1. Similarly, A increases with donor concentration when [D] < [A] up to A = 1, then remains saturated at [D] > [A]. Note that only Fc/D, Fa/D (top graph), and Eapp (bottom graph) maintain the same tendencies as D, whereas Fc/A and Fd/A correlate with A. In contrast, Fc, F/D, FRETN, and NFRET do not correlate consistently with the degrees of interaction for Type 3 experiments.

1. E_app computed by the E-FRET method is linearly proportional to the degree of donor interaction.
   
2. Group 1 indices F_c/D and F_a/D reflect the degree of donor interaction nonlinearly.
   
3. Group 2 indices F_c/A and F_d/A are proportional to the acceptor occupancy.
   
4. Group 3 indices FRETN and N_FRET are not indicative of the degrees of molecular interactions in Type 3 experiments.
   

Overall, only E_app (and E_corr if photobleaching correction is desired) fulfills two goals of FRET imaging: proportionality to the degree of molecular interaction (with respect to donor) and the independence of the optical parameters of the imaging system.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX: GLOSSARY ACKNOWLEDGEMENTS REFERENCES

 
FRET efficiency imaging
Because imaging of FRET based on the sensitized emission of acceptor does not immediately allow calculation of the apparent FRET efficiency E_app, various indices and ratios have been used to visualize FRET. We use the E_app symbol instead of E to distinguish it from the specific transfer efficiency of pure interacting complex (E_max). Here we define and demonstrate a practical method to visualize sensitized-emission imaging data in terms of E_app. Our method, designated E-FRET, allows visualization of FRET similarly to the donor-recovery method, but without the inherent drawbacks. Furthermore, we approach another problem plaguing timelapse and three-dimensional imaging of FRET, which is the degradation of measurements due to gradual photobleaching of the sample. E-FRET provides for appropriate correction such that the corrected FRET efficiency E_corr can be calculated as if photobleaching did not occur. All calculations are based on 3-cube imaging allowing easy adaptation to existing microscopes. E_app and E_corr allow easy evaluation of the relative magnitude of the FRET effect and facilitate comparison of FRET data between laboratories, independent of the instrumentation involved.

E-FRET unifies ratiometric FRET methods with the donor recovery after acceptor photobleaching method. The distinct advantage of the methodology presented here rests in experimental calibration of the G parameter, which is necessary for calculating FRET efficiency from sensitized-emission imaging. G was introduced to link sensitized emission of acceptor with the concomitant quenching of donor (Gordon et al., 1998). We found that calculation of G from physical constants allowed only a rough estimate due to the large error margin inherent in the determination of quantum yields in cells, and in the determination of the spectral transmission characteristics of the imaging path of the microscope (Zal et al., 2002). Instead we calibrate G directly as the ratio of sensitized emission in a reference sample to the donor recovery after acceptor photobleaching. We demonstrate that the FRET construct for G calibration need not be the same as for the experiment and may have different E_max, which does not need to be known. Determination of G for a particular imaging system does not require any additional equipment other than what is typically necessary for 3-cube imaging. Once calibrated, G is applicable to subsequent calculations of E_app and E_corr for experiments relying on the same donor and acceptor fluorophores as long as timing of exposures in all channels is kept proportional. An analogous approach should be directly applicable to measure G as the ratio of the change of sensitized emission to donor recovery after enzymatic digestion of a Type 2 FRET construct (data not shown). This will allow determination of G for photo-stable acceptors.

G estimated from optical parameters of the imaging system (Eq. 14) and the formula given by Eq. 13 allowed us in a previous study to convert, for the first time, readings of the F_a/D index to FRET efficiency values (Zal et al., 2002). A formula for the E_app equivalent (E_D) was presented recently (Hoppe et al., 2002) but required back-calculation of instrumental parameters based on external determination of E_max. E_D relied on two parameters: , which is the ratio of the acceptor extinction coefficient to the donor at donor excitation and , which is a proportionality constant, similar in concept but different from G in that G = /. Both and had to be calculated from the known stoichiometry of interaction and the specific FRET efficiency of the interaction E_C (equivalent to E_max), which was obtained from lifetime measurements. Such measurements are usually impractical without access to FLIM instrumentation or biochemical purification of the complex. In our photobleaching calibration method, knowledge of E_max is not necessary and G can be calibrated without additional instrumentation. The FR ratio was proposed for computation of effective FRET efficiency defined with respect to acceptor as E_maxA (Erickson et al., 2001). FR is different from the classic definition of FRET efficiency, although it is useful for monitoring _A.

Linear crosstalk correction is an integral part of E-FRET calculations and is built into the corresponding formulae based on previous work (Youvan et al., 1997). Elangovan and co-workers observed nonlinear bleedthrough between CFP and dsRED1 or Alexa488 and Cy3 which prompted tabulated crosstalk correction depending on fluorescence intensity (Elangovan et al., 2003). It is not clear whether factors intrinsic to fluorophores or related to the detection devices caused this effect. Therefore the constancy of bleedthrough factors has to be tested for new donor-acceptor pairs and imaging systems. In this respect it is important to note that the bleedthrough coefficients for ECFP and EYFP were indeed remarkably constant across a wide range of concentrations in cells, in different intracellular compartments, and under clustering conditions (data not shown; but see Zal et al., 2002), when measured using CCD cameras with flatfield correction and intraimage background subtraction.

Comparison of E-FRET with other FRET methods
A remarkable variety of formulae have been proposed for reporting FRET based on sensitized-emission imaging (Berney and Danuser, 2003). The reasons behind the proposal of differing indices are at least twofold. The first is the need for simplicity: Type 1 (internal FRET) and some Type 2 (digestible linker) experiments require only two-image ratioing to achieve the simplest possible, concentration-independent, FRET index. In contrast, Type 3 (heterologous) and some Type 2 experiments require explicit crosstalk subtraction demanding three-image calculations. The second reason behind the proliferation of FRET methods is due to conflicting criteria for interpreting changes in FRET in Type 3 experiments. For Type 3 experiments, the general question asked by the experimenter, whether donor-labeled species X and acceptor-labeled Y physically interact, can be broken into more specific and quantitative problems: 1), if and where a significant proportion of X is in the proximity of Y, and 2), if and where a significant proportion of Y is in proximity of X, 3), is this proximity a biologically relevant molecular interaction or a random collision? Questions 1 and 2 are not equivalent for Type 3 experiments. For instance, if Y is present in excess over X, a high affinity interaction of the two will give 100% interaction with respect to X and a low degree of interaction with respect to Y, and vice versa. From this point of view we distinguished three categories of FRET ratio indices to compare with E-FRET with respect to correlation with the degrees of molecular interaction. Group 1 indices are denominated by donor fluorescence, group 2 indices are denominated by acceptor fluorescence, and group 3 indices are denominated by both donor and acceptor.

Comparison of E-FRET with other FRET ratios through mathematical modeling of Type 3 experiments demonstrated that group 1 ratios F_c/D and F_a/D as well as the E-FRET formula reflect the donor occupancy by acceptor. Therefore these measures should be used for experiments where acceptor is available at or above stoichiometric concentration over donor, such that it is the affinity of interaction, not the acceptor availability which is limiting. Group 2 ratios F_c/A and F_d/A correlate with the acceptor occupancy by donor and thus are preferable for experiments where the acceptor-labeled species is limiting. Unfortunately, this also limits the intensity of sensitized emission, making group 2 ratios error-prone (data not shown). Group 3 indices FRETN and N_FRET were concentration-dependent and did not consistently correlate with either degree of interaction.

There are two main advantages of E_app