Fluorescence resonance energy transfer (FRET) by acceptor photobleaching is a simple but effective tool for measurements of protein–protein interactions. Until recently, it has been restricted to qualitative or relative assessments owing to the spectral bleed-through contamination resulting from fluorescence overlap between the donor and the acceptor. In this paper, we report a quantitative algorithm that combines the spectral unmixing technique with FRET by acceptor photobleaching. By spectrally unmixing the emissions before and after photobleaching, it is possible to resolve the spectral bleed-through and retrieve the FRET efficiency/interaction distance quantitatively. Using a human keratinocyte cell line transfected with cyan fluorescent protein (CFP)- and yellow fluorescent protein (YFP)-tagged Cx26 connexins as an example, FRET information at homotypic gap junctions is measured and compared with well-established methods. Results indicate that the new approach is sensitive, flexible, instrument independent and solely FRET dependent. It can achieve FRET estimations similar to that from a sensitized emission FRET method. This approach has a great advantage in providing the relative concentrations of the donor and the acceptor; this is, for example, very important in the comparative study of cell populations with variable expression levels.
Fluorescence resonance energy transfer (FRET), also known as Förster resonance energy transfer, is a photophysical process that involves non-radiative transfer of excited-state energy from an initially excited fluorescent donor to a fluorescent acceptor, which in turn emits a photon at longer wavelength (Clegg, 1992; Lakowicz, 1999). FRET between the donor and the acceptor (D–A) can be characterized by the efficiency of energy transfer (E), which is measured as the relative fluorescence of a donor in the presence and the absence of its acceptor (Clegg, 1992; Lakowicz, 1999). As FRET only happens within a certain distance (< 10 nm), and E is very sensitive to the distance change, FRET microscopy enables assessments of protein–protein interactions on the scale of several nanometres.
FRET measurement is mainly based on Förster theory, which defines the energy transfer on the base of one donor and one acceptor system. FRET detection techniques can be generally classified into fluorescence-decay-kinetics-based and intensity-based approaches (Wouters et al., 1998; Lippincott-Schwartz et al., 2001; Eidne et al., 2002). Fluorescence-decay-kinetics methods derive the FRET information by measuring the donor photobleaching lifetime or the donor fluorescence lifetime changes in the presence of the acceptor. The intensity-based approaches retrieve the steady-state FRET information by measuring either the acceptor-sensitized emission (seFRET) or the donor fluorescence variation with acceptor photobleaching (also called acceptor depletion FRET or adFRET) (Wouters et al., 1998; Wu & Brand, 1994; Sekar & Periasamy, 2003).
seFRET provides a non-destructive quantification of the protein–protein proximity and assessment of their interaction distribution within live cells. It measures the fluorescent emission change of a donor due to the presence of its acceptor, i.e. the donor emission decreases while the acceptor emission is enhanced. The major problem associated with seFRET detection is to separate the spectral bleed-through (SBT), i.e. the contribution of donor and acceptor fluorescence emission to the FRET channel. Various methods introducing different detection strategies have been reported or reviewed elsewhere (Wouters et al., 1998; Wu & Brand, 1994; Lippincott-Schwartz et al., 2001; Eidne et al., 2002; Berney & Danuser, 2003). Gordon et al. (1998) used three filter sets on a standard fluorescence microscope system and two controls (the donor-only and the acceptor-only specimens) to correct SBT and the dependence of FRET on the emission levels of donors and acceptors. Xia & Liu (2001) further improved the algorithm by taking into account the protein expression levels, which in turn gives a more consistent FRET measurement. Recently, Elangovan et al. (2003) proposed a new algorithm (E-seFRET) applicable for both confocal and epifluorescence microscopes with single-photon or multiphoton excitation. This method uses one filter set and two laser lines with two control specimens to remove both the donor and the acceptor SBT. Because the process associates the fluorophore expression levels of control cells with that of the test specimen, this approach provides a more sensitive basis to estimate the distributions of FRET efficiency and D–A distances across the image.
adFRET, by contrast, is based on the fact that photobleaching acceptors will irreversibly block the energy transfer and de-quench donors. Assuming that the photophysical process of acceptor photobleaching is the only local environmental change, a relative increase in donor fluorescence before and after acceptor photobleaching is solely determined by FRET (Karpova et al., 2003), independent of environmental factors such as autofluorescence, the acceptor's interaction with other molecular entities or instrument settings. Therefore, adFRET provides a simple but potentially accurate FRET measurement. However, because photobleaching is an irreversible photochemical process, this approach is limited to in vitro applications with fixed specimens. Another difficulty hindering the quantitative FRET measurement is SBT, including (1) the acceptor emission bleed-through into the donor channel (emission SBT), and (2) the donor photobleaching during the acceptor depletion (photobleaching SBT). In traditional microscopy, two hardware approaches are used to tackle SBTs, the emission separation and the excitation separation (Zimmermann et al., 2003). The emission separation is achieved by choosing an appropriate optical band-pass filter, which only transmits the specific part of a fluorophore's spectrum. The fluorescence acquired in this channel is usually taken as the emission of the fluorophore, given that it has dominant emission to other fluorophores. The excitation separation is realized by the sequential imaging approach. Relying on the absorption spectrum difference of fluorochromes, multiple laser lines are employed with each line exciting only a chosen fluorochrome on a certain scan track. Thus fluorescence emissions from different fluorochromes are temporally separated. Nevertheless, the available D–A pairs are not always distinct enough to show emission dominance, neither are laser lines precise enough to excite selectively. Taking CFP and YFP as an example, whereas the 514-nm argon laser can excite YFP only, the 458-nm argon laser tends to excite both CFP and YFP, and the emission SBT of CFP into the YFP channel can be theoretically as much as 23% (with spectral channel settings: donor, 495.5 ± 5.5 nm; acceptor, 538.5 ± 5.5 nm). Therefore, hardware solutions are insufficient for quantitative FRET assessment; emission SBT compromises the donor fluorescence enhancement with the acceptor fluorescence decrease, and photobleaching SBT eliminates both fluorophores. So far, adFRET is more or less restricted to either qualitative measurement (Kenworthy & Edidin, 1998; Wouters et al., 1998; Mas et al., 2000; Siegel et al., 2000) or relative measurement (Majoul et al., 2002; Zaccolo et al., 2000).
Spectral unmixing is a well-established image processing methodology in remote sensing. Recently, it has been introduced into the field of cell biology to explore multispectral fluorescence signatures within cells and organisms. It is also employed to separate molecules labelled with different fluorochromes within a cell for the study of molecular motility, co-localization and interaction (Tsurui et al., 2000; Dickinson et al., 2001; Hiraoka et al., 2002; Zimmermann et al., 2003). The principle of linear spectral unmixing is based on the approximation that spectral signatures of a test sample are the sum of a linear combination of the abundance-weighted spectra of constituent pure classes (Petrou & Foschi, 1999). Using the emission spectra of specified pure fluorochromes as a reference, the fluorescence intensity of the corresponding fluorochrome within a mixture can therefore be precisely determined from its composite spectrum. Linear spectral unmixing provides a unique approach to tackle SBT.
Gap junctions are clusters of double-membrane channels that create hydrophilic pores across the cell membranes. Gap junctions are formed between two adjacent cells across a narrow extracellular gap by two hemi-channel trans-membrane protein structures termed connexons. Each connexon is made up from six trans-membrane protein subunits named connexins, which are four trans-membrane spanning proteins with intracellular NH2- and COOH-termini placed on the cytoplasmic membrane surface. Because the intercellular channel allows the diffusion-driven transfer of small cytoplasmic molecules, ions and second messengers, gap junctions play important roles in the co-ordination of development, cellular homeostasis and tissue functions (Unger et al., 1999; Quist et al., 2000; Common et al., 2002; Falk, 2002).
Studies have shown that the structure of a connexon resembles a hexameric barrel formed by six connexins or 24 α-helices. The height of the barrel (the length of a connexon) is about 7.5 nm, which makes a gap junction channel 15 nm in length and 7 nm in diameter in the membrane region (Unger et al., 1999). Normally, gap junction channels cluster on the cell surface into plaques, which are tightly packed two-dimensional (2D) arrays with about 9 nm between adjacent channels (Goodenough et al., 1996). Such proximity between channels makes FRET an ideal tool to investigate the formation and the interaction of homomeric/heteromeric connexons.
In this paper, we report a new quantitative algorithm that combines linear spectral unmixing with acceptor photobleaching FRET (u-adFRET). This method relies on linear spectral unmixing to separate donors and acceptors before and after photobleaching, and measures the FRET from the unmixed donor population. Because SBT is tackled in advance, the donor enhancement revealed by acceptor photobleaching is solely from FRET. As spectral unmixing calculates relative concentrations of individual components, u-adFRET provides not only E and interaction distance, but also relative concentrations of the excited donor/acceptor populations, which is of great advantage in studying statistically cell populations with variable expression levels. Cells with gap junctions formed by CFP/YFP-tagged Cx26 homomeric connexons are used as a demonstration, upon which a comparison between adFRET, u-adFRET and an improved E-seFRET (Elangovan et al., 2003) is also conducted as a validation of u-adFRET. Finally, we report difficulties experienced in FRET measurements using CFP and GFP used as a D–A pair.
2. Materials and methods
2.1. u-adFRET algorithm
The image acquisition required by u-adFRET includes a time sequence with a number of spectral channels. The photobleaching starts at a certain time point when the imaging laser is turned off and the image acquisition is adjourned. After photobleaching, the imaging laser is turned on again to finish the rest of the sequence. Eight spectral channels with spectra covering significant emission parts of CFP and YFP are used to maximize the unmixing accuracy.
The linear spectral unmixing algorithm can be expressed as
Fm(x, y, λ) = d(x, y)Fd(λ) + a(x, y)Fa(λ)(1)
where d(x, y) and a(x, y) are unknown abundance factors of the two fluorochromes at pixel location (x, y), whose spectral responses are expressed as Fd(λ) and Fa(λ), respectively (subscripts d and a imply the donor and the acceptor), and Fm(x, y, λ) is the spectral response of a test sample, which is normalized from the detected emission to eliminate the variation influence of absolute intensities. Fd(λ) and Fa(λ) are measured using single fluorochrome specimens (controls). Equation (1) is applicable when fluorochromes composed in a test sample do not have chemical interaction between each other, which enables the spectrum of controls to be used in spectral decomposition. To avoid interference from the environment, controls are made from the same specimen under exactly the same conditions, and are imaged under exactly the same spectral settings whose influence is cancelled out during the linear unmixing process.
Theoretically, to resolve Eq. (1) with two unknown abundances, emissions from two spectral channels are the minimum requirement. In practice, however, because of the imperfection of the linear unmixing model, and low signal-to-noise ratio in fluorescence imaging, two spectral channels often produce rough approximations of the true values. With redundant spectral information, applications of the least-squares algorithm are especially beneficial, as the best fit relies on the overall detected spectrum rather than any single channel. The contribution of each channel is only weighted one part over the total number of channels, and any noisy channel has only limited influence on the estimation. Estimations of d(x, y) and a(x, y) using a least-squares technique are given by Eq. (A4).
The strength of FRET can be measured by net FRET intensity, the rate of energy transfer and E (FRET efficiency) (Clegg, 1992; Gordon et al., 1998). In this paper, we use E as a FRET measure because it is directly linked to the D–A proximity (R).
where R0 is called the Förster distance, which is defined as the D–A distance when E = 50%. R0 is determined by spectroscopic properties of a D–A pair (Clegg, 1992). In u-adFRET, E is calculated by (Appendix A1)
where fd(x, y) and are fluorescence of the donor before and after photobleaching, d(x, y) and dph(x,y) are donor abundance factors before and after photobleaching, and fmax(x,y) and are maximum spectral emissions of a test sample before and after photobleaching.
Relative concentrations are an important parameter in quantitative FRET measurements, especially when FRET efficiencies measured from different cells or different parts of a cell need to be compared (Erickson & Cerione, 1991; Kenworthy & Edidin, 1998; Zacharias et al., 2002; Berney & Danuser, 2003; Wallrabe et al., 2003). The linear spectral unmixing before photobleaching gives relative concentrations of emitting fluorophores. It does not, however, include the interacting donors, which only become visible after photobleaching. Assuming that photobleaching completely eliminates the acceptor emission, relative concentrations dc(x, y) and ac(x,y) can be deduced from emissions of the acceptor before photobleaching and the donor after photobleaching (Appendix A1):
where fmax(x, y) and are maximum spectral emissions of a test sample before and after photobleaching, dph(x,y) is the donor abundance factor after photobleaching, and a(x,y) is the acceptor abundance factor before photobleaching.
2.2. Modifications to the E-seFRET algorithm
E-seFRET proposed by Elangovan et al. (2003) uses two laser lines, three samples (two controls and one test specimen), two detection channels and the sequential imaging technique to resolve the net FRET intensity. Because E-seFRET is based on an assumption that the test specimen and the controls are imaged under the same experimental conditions (such as the same excitation and the same PMT gain), the algorithm is not always convenient to implement. Different fluorophores have different extinction ratios and different quantum yields, which often lead to different emission levels even when they are expressed at the same level. In extreme circumstances, the fluorescence of a particular specimen would drop out of the detector's dynamic range as a result of saturation or a poor signal-to-noise ratio. Therefore, we suggest relieving restrictions to the excitation and partially freeing the gain control, and compensating the variation during processing.
Referring to Appendix A2, the net FRET (PFRET) is
where GiJk is the PMT gain with i, J and k standing for specimen (d, a and m), laser line (D and A) and detecting channel (d and a), respectively, Ie(i, J) corresponds to laser intensity of the indicated excitation, m stands for the test sample, and d and a are the donor and the acceptor, and PFRET(x, y), UFRET(x, y), DSBT(x, y) and ASBT(x, y) are defined by Elangovan et al. (2003) (see Table A1).
Because the META detector array shares the same gain setting, changing gain will not generate any amplification difference between channels. When gains on different scan tracks are set to the same gain, its influence will be completely cancelled out during the calculation:
E can be derived as
where Ed(λd) and Ed(λa) are spectral responses of the donor at the donor and acceptor channels (λd and λa), respectively.
Laser scanning confocal microscope LSM 510 META (Carl Zeiss Ltd) allows multispectral images to be collected simultaneously without compromising resolution and efficiency. The META spectral detectors (32 PMTs in a linear array) are aligned in such a way that they cover any emission wavelength between 378.4 nm and 720.8 nm, with up to 11-nm spectral resolution and a maximum output of eight spectral channels (Chs). An optical grating is used to disperse and project the emission so that each of the 32 detectors is spatially addressed to a certain wavelength. As detectors are made and assembled in the same procedure, they have approximately the same performance. The system is designed in such a way that all 32 channels share the same PMT gain, the same pinhole and the same optical path, so that the system transmission efficiency has the same influence upon all detectors. Finally, the flexibility to choose emission detection wavelength and bandwidth enables users to choose the best emission windows of their fluorophores.
2.4. Cx26–GFP cDNA constructs
cDNA sequences of the fluorescent reporter proteins CFP, GFP and YFP were fused in-frame to the COOH-terminus of the human wild-type GJB2 gene encoding Cx26. The authentic connexin stop codon was changed from TGA to GGA by PCR using the primers with restriction site sequences HindIII and SalI (underlined in the primer sequences), 5′-GCGAAGCTTATGGATTGGGG for forward primer and 5′-GCGGTCGACCATCCAACTGGCTTTTTTG for reverse primer. Amplified connexin cDNA was cloned into the HindIII and SalI restricted vectors pEGFP-N1, pECFP-N1 and pEYFP-N1 (Clontech, Hampshire, U.K.). All constructs were verified by restriction digestion and automated DNA sequencing.
2.5. Cell culture, transfection and cell fixation
The human keratinocyte cell line (NEB1) (Morley et al., 1995) was used throughout this study. Cell lines were cultured in 3 : 1 Dulbecco's modified Eagle's medium (DMEM): Ham F12 medium, supplemented with 10% fetal calf serum (FCS), 0.4 µg mL−1 hydrocortisone, 5 µg mL−1 insulin, 10 ng mL−1 epidermal growth factor, 10 × 10−10m choleratoxin, 5 µg mL−1 transferin, 2 × 10−11m lyothyronine and 100 µg mL−1 penicillin–streptomycin.
Cells were transfected with Cx26–GFP, Cx26–CFP and/or Cx26–YFP constructs using Transfast (Promega, Southampton, U.K.). Cells at 1 × 105 per 13-mm cover-slip were transfected with 1 µg of plasmid DNA per construct in 1 : 2 Transfast reagent. Twenty-four hours post-transfection, cells were fixed with 4% buffered paraformaldehyde for 15 min and were mounted in Mowiol reagent containing 10% Mowiol 4-88 (Calbiochem, Beeston, U.K.), 25% glycerol, and 2.5% 1.4-diazabicyclo [2.2.2] octane (Sigma, Poole, U.K.) in 50 mm Tris/HCl, pH 8.5. Fixed cells were kept at −20 °C until being imaged.
3. Results and discussion
3.1. u-adFRET processing results
A typical u-adFRET setting is shown in Table 1(a). The excitation of the imaging laser (argon 458 nm) is adjusted so that photobleaching throughout the acquisition is negligible. Acceptor photobleaching, which starts after time point 15, is repeated for 100 times over preselected ROIs, making sure that the overall acceptor population within each ROI is eliminated.
Table 1. Confocal microscope settings.
(a) Microscope settings for u-adFRET/adFRET
(b) Microscope settings for E-seFRET
META spectral settings (nm)
Chs2: 485–496 nm
Chs6: 528–538 nm
458 nm and 514 nm (multitrack)
Plan-Apochromat 63×/1.4 Oil Ph3
5.26 Airy Units
7 (2.88 µs pixel−1)
69.1 × 40.6 × 3 µm ↔ 484 × 284 × 12 bit
63×/1.4 Oil Ph3
5.26 Airy Units
7 (2.88 µs pixel−1)
Total time points
30 (4.3 s frame−1)
Photobleaching time point
15 (repeat 100 times −0.57 ms pixel−1)
69.1 × 40.6 × 3 µm ↔ 484 × 284 × 12 bit
Mixed sample imaging
Figure 1 shows part of the processing results from NEB1 cells co-expressed with Cx26–CFP and Cx26–YFP fusion proteins. E, F and G in Fig. 1(d) indicate plaques of intracellular gap junctions formed by homomeric connexons. Because photobleaching was only implemented in selected windows (red areas in Fig. 1d), the FRET efficiency calculated by u-adFRET (Fig. 1e) is limited to those regions, which contrasts with the FRET efficiency calculated by E-seFRET that covers the whole image (Fig. 1f).
Quantitative assessment can be made by sampling within ROIs (A–G in Fig. 1d). Figure 1(h) demonstrates the mean unmixing error within ROI A. Figure 1(i) shows the time sequence of the mean fluorescence of donors and acceptors within ROI A, in comparison with the mean background (ROI H) and the mean fluorescence of an unbleached region (ROI I). The donor emission enhancement is examined using a t-test. Only when the emission difference before and after photobleaching is significant are the FRET results validated (Table 2). During data processing, it is found that pixel-based E distributions are sometimes ‘noisy’, especially when the donor enhancement after photobleaching is comparable with the random noise level (including shot noise and PMT dark noise). It is partially caused by the way that E is calculated, which is vulnerable to noise. In u-adFRET, the problem is addressed by averaging intensities within ROIs before and after photobleaching to calculate the mean E.
Table 2. Mean value from ROI A using u-adFRET and E-seFRET.
ROI A (141, 98) 9 × 9
Mean fluorophore concentration (D:A)
60.7%: 39.3 ± 2.1% (1σ)
Mean unmixing error (prebleaching)
4.1 ± 2.7% (1σ)
28.1 ± 4.5% (1σ)
27.7 ± 2.4%
Significance of E (P < 0.01)
Slow photobleaching during the imaging
Mean D–A distance
Mean of relative photobleaching
92.5 ± 19% (1σ)
Because CFP and YFP proteins are tagged to the COOH termini of the Cx26, FRET across a gap junction is very weak (E < 0.2%). By contrast, the intercellular parts are more favourable for FRET, as the interaction proximity is usually less than 7 nm, which is more or less confirmed in Table 2. When connexins are tagged with different fluorophores, FRET results over a certain cell population can be used to confirm the presence of homomeric/heteromeric connexons.
3.2. Comparison of adFRET, E-seFRET and u-adFRET
As cell expression levels, fluorophore concentrations, media variation and instrument instability will introduce uncertainty during image acquisition, a fair comparison should be performed on the same test sample with the same field of view, the same spectral channel setting, single microscope mounting and one focusing adjustment (Table 1). After setting up the system, E-seFRET was performed, with the images being acquired in standard sequential scans with the donor control, the acceptor control and a test sample, respectively. The image was averaged over 16 times to enhance the signal-to-noise ratio. META channels were used not only to simplify the post-processing (section 2.2) but also to make the result comparable with other methods. After the acquisition of E-seFRET, a time-sequence with acceptor photobleaching was acquired (section 2.1), with which both u-adFRET and adFRET can be applied. Figure 2 shows the processing results from three FRET methods.
Based on the results shown in Fig. 2 and Table 2, we may conclude that:
1E values calculated from E-seFRET and u-adFRET appear to be significantly larger than those from adFRET, which confirms that SBT in the donor channel will reduce the donor emission enhancement after photobleaching, and in turn reduce E. From this perspective, E-seFRET and u-adFRET provide higher detection sensitivity and wider dynamic range, which are very important for the detection of weak signals generated by long-range interactions, low-level interactions or low fluorophore concentration.
2E values from E-seFRET and u-adFRET are not significantly different, which demonstrates that both algorithms have equally eliminated SBT and have similar sensitivity. Although E should be independent of detections, inaccuracy introduced by factors such as model, signal-to-noise ratio and photobleaching by imaging laser contribute to the differences of different estimations.
3u-adFRET is easy to implement and is independent of instrument settings (such as PMT gain and excitation). On the other hand, E-seFRET requires a well-characterized microscope system, as the measurement is directly linked to the system parameters such as laser intensities and PMT gains.
4Apart from using the same filter set for references and samples, u-adFRET gives more flexibility for the experimental set-up. For example, low excitation with high PMT gain is often used to reduce photobleaching by the imaging laser without compromising the signal-to-noise ratio. As u-adFRET uses single-track scanning, the laser intensity and the PMT gain are two independent parameters for tackling photobleaching and signal-to-noise ratio. By contrast, in E-seFRET, they are restricted by the need to balance between the two scan tracks.
5E values calculated by u-adFRET are independent of spectral settings of emission channels (Fig. 3), i.e. the selection of the donor/acceptor channels is no longer required for FRET measurements. By contrast, they are still essential in the other two approaches.
6u-adFRET can only be applied to fixed specimens, with the exception of live cells when whole cell photobleaching is practical (cell size and motility). E-seFRET, by contrast, is more flexible, and can be applied to both live and fixed cells, which opens the possibility for dynamic FRET measurement.
7The availability of META spectral detectors simplifies the acquisition as well as the processing. Nevertheless, u-adFRET is not restricted to the LSM 510 META. As with E-seFRET, the algorithm can be implemented on any confocal system with standard settings.
8Similar to the E-seFRET, u-adFRET can be applied to multiphoton imaging. However, because fluorophores usually have very broad absorption bands under a multiphoton excitation, the selective acceptor photobleaching still needs to be done by a single-photon laser.
3.3. Evaluation of u-adFRET methodology
Ideally, u-adFRET should be evaluated using control samples with known concentrations and known E. Finding such samples, however, is very difficult. We used Cx26–CFP and Cx26–YFP transfected cells as single fluorophore protein controls and expected to achieve 0%E and 100% : 0% relative concentrations in both cases. The calibrations were carried under the same settings as given in Table 1. The samples are prepared under the same conditions described under section 2.5. The results shown in Fig. 4(c,f) demonstrate that the u-adFRET outcomes matches prediction; both relative concentrations are correctly calculated, and FRET is not significant in the photobleaching regions. The residual unmixing errors shown in Fig. 4(b,d) occur at pixels where the signal-to-noise ratio is very low.
u-adFRET can also be validated by comparing with the well-established FRET approaches, such as E-seFRET. The results shown in Fig. 2 indicate that two processes produced very similar results.
3.4. Comments on linear spectral unmixing
In confocal microscopy, the fluorescence signal is usually weak. The variation introduced by random noise (such as shot noise and PMT dark current noise) will influence the unmixing accuracy. Improvement of spectral unmixing may be achieved by either enhancing the signal-to-noise ratio or increasing the spectral sampling redundancy. The signal-to-noise ratio can be improved by increasing the laser intensity or averaging images. However, these can cause sample photobleaching, and prolong image acquisition, respectively. Increasing the spectral sampling redundancy (or the number of parallel detection channels), by contrast, does not incur those disadvantages, as all spectral information is acquired simultaneously. Examples presented above use eight channels with equally spaced narrow bandwidth (11 nm) and continuous spectral coverage. This is, however, not compulsory in u-adFRET. The spectral bandwidth of each channel is defined by the strength of fluorescence and the emission range. As the emission of a fluorophore is usually over 100 nm wide, spectral bandwidth provides flexibility to meet signal-to-noise requirements.
Spectral unmixing accuracy may be examined by studying the unmixing fit error shown in Fig. 1(h). Significant unmixing error usually indicates either a very poor signal-to-noise ratio or a discrepancy from the original reference spectra. The former can be easily identified by the emission levels in ROIs, and the latter is likely to be caused by either the variation in sample preparation or the existence of unknown fluorescence sources. Using the latter feature, u-adFRET provides a solution to monitor fluorophore spectral changes, identify unknown fluorochrome compositions and measure autofluorescence. Autofluorescence is a general term for the fluorescence emission from media, substrate or non-tagged cells. Under normal conditions, autofluorescence of cells should be weak and negligible (such as the case shown in Fig. 1i). However, certain cell types and media could generate strong emissions at certain excitation wavelengths. When autofluorescence is not negligible, its influence on the abundance factors and the FRET evaluation must be considered. In u-adFRET, it can be conveniently treated as the third component, whose emission influence can in turn be eliminated by the unmixing algorithm.
3.5. Comments on the selection of donor–acceptor pairs
An efficient FRET signal relies on an appropriate selection of D–A fluorochromes with the following features: (1) the donor fluorophore should have a sufficiently long lifetime so that donor electrons can stay in the excited state long enough for the process of energy transfer; (2) there is enough spectral overlap between the emission of a donor and the absorption of its acceptor; (3) favourable relative orientation between the emission dipole of a donor and the absorption dipole of its acceptor; (4) the D–A distance is within a certain range (< 10 nm); and (5) a donor has a relatively high quantum yield, and its acceptor has a reasonably high extinction coefficient.
Increasing spectral overlap will undoubtedly increase the FRET sensitivity. With the help of u-adFRET, SBT between two fluorophores with very similar emission spectrum is no longer a problem in FRET measurement. We have successfully separated CFP–GFP and GFP–YFP mixtures (data are not shown). Are we free to use new D–A pairs with more favourable spectral overlaps? Are they going to increase the detection sensitivity? Bearing in mind these questions, we co-expressed Cx26–CFP and Cx26–GFP in NEB1 cells, using the co-expressed Cx26–CFP and Cx26–YFP cells as a control. Under identical conditions, the experiment was repeated three times over 30 gap-junction-like ROIs on ten cells (Fig. 5). Whereas the latter demonstrated strong E and reasonable linearity, the former did not reveal much FRET. The limited FRET efficiency shows a poor linear fit and seems independent of the relative acceptor concentration. As the connexon structure on a gap junction is supposed to be identical for both the control and the test sample, the interaction distance between fluorophores is not expected to have large difference. How can we explain such a contradiction? As the only difference is the D–A pair, we conclude that CFP and GFP are not a reliable D–A pair. As very little energy is transferred between CFP and GFP, we speculate that this phenomenon may be related to the similarity of the energy level of the first excited states of the two fluorophores, which hampers the energy transfer. Further investigation is under way to explore the details.
u-adFRET is a quantitative approach to FRET measurements using acceptor photobleaching. It addresses SBT, a major issue in FRET measurements, by introducing a spectral unmixing technique. With the test sample being unmixed before FRET analyses, SBT is clearly eliminated. As a result, FRET measurements are no longer dependent upon the setting of the donor/acceptor channels. The general reasoning behind u-adFRET is easy to follow, the actual image acquisition and data processing are straightforward, flexible and instrument independent, and the results obtained with u-adFRET are comparable with other well-established methods. The u-adFRET calculation provides not only FRET efficiency and interaction distances, but also the relative concentrations. Such an association makes u-adFRET an important approach if a global FRET comparison within the cell population becomes necessary, or if the detection of interaction distance varies during a biological process.
We thank Tamara Cavanna for her helpful suggestions. We would also like to thank the Biotechnology and Biological Sciences Research Council for supporting the connexin project.
A1. u-adFRET algorithm
The fluorescence emission spectrum of a mixed specimen is an addition of the abundance-weighted spectral response of all constituents (Hiraoka et al., 2002). In the two-element case,
Fm(x, y, λ) =d(x, y)Fd(λ) +a(x, y)Fa(λ)((A1))
The estimation of abundance factors is determined by the least-squares fit defined as (Gu & Anderson, 2003):
where δ is the least-squares error and n is the number of spectral channels. Accordingly, the first derivatives of δ will be zero:
Therefore, the unconstrained abundance factors are resolved as:
The fluorescence of each fluorophore can be decomposed from Eq. (A1) as
where fmax(x, y) is the maximum emission of a test sample in all spectral channels.
Instead of using absolute emission levels, the abundance factors from spectral unmixing give the relative concentration of two fluorophores. However, those non-radiative donors involved in FRET are invisible without photobleaching. Assuming that photobleaching can completely deplete the acceptor emission, the relative concentrations can be deduced from combined emissions from the acceptor before photobleaching and the donor after photobleaching:
where dc(x, y) and ac(x, y) are relative concentrations of fluorophores. Taking into account the absolute molecular concentration, which is proportional to the emission, the abundance mappings of the donor and the acceptor across an image are
E can be derived directly from the unmixed donor emission before/after photobleaching (Clegg, 1992):
where PFRET0(x, y) is net FRET intensity, UFRET0(x, y) is the detected FRET signal from the FRET channel, and DSBT0(x, y) and 0(x, y) are SBTs from the donor and the acceptor. The algorithm is based on the precondition that all image acquisitions are based on the same microscope conditions, including the excitation laser power and PMT gains (Elangovan et al., 2003). However, it is not always convenient to use the same settings. Owing to different quantum efficiencies and extinction ratios, cells will fluoresce differently even when they have the same expression level and under the same excitation. Assuming that fluorescence is proportional to the excitation intensity, we have
where GiJk is the PMT gain with i, J and k standing for a specimen, a laser line and a detecting channel, respectively, and Ie(i, J) corresponds to the laser intensity of an indicated excitation. Substituting Eq. (A10), a more general form of Eq. (A9) is
With a META detector array, it is possible to set GdDd = GdDa, GmDa = GmDd = GmAa, and GaDa = GaAa, then