Distribution of a Glycosylphosphatidylinositol-anchored Protein at the Apical Surface of MDCK Cells Examined at a Resolution of <100 Å Using Imaging Fluorescence Resonance Energy Transfer

The full-length 5′ NT cDNA from rat liver (clone pcNT341) was the generous gift of Dr. Y. Ikehara (Misumi et al., 1990). pcNT341 was inserted into EcoRI site of pCB6 (Brewer, 1994) modified to contain a portion of the Bluescript multicloning site. MDCK cells (type II) were transfected using a calcium phosphate precipitation method (Weisz et al., 1992) and selected in medium containing 500 μg/ml G418 (GIBCO BRL, Gaithersburg, MD). Positive clones were isolated using cloning rings and screened by indirect immunofluorescence microscopy. One of the positive clones was then subcloned by cell sorting, followed by seeding at limiting dilution with untransfected cells.

After cloning, cells were maintained in DME (GIBCO BRL, Gaithersburg, MD) supplemented with 10% fetal calf serum (INTERGEN Co., Purchase, NY), nonessential amino acids (GIBCO BRL), and 300 μg/ml G418. Propagation stocks were passaged at a 1:50 dilution every 4–6 d. Cells for experiments were plated onto sterile coverslips at a 1:5 dilution (∼1 × 10⁶ cells/10-cm plate, six coverslips/plate, transferred to six-well dishes the following day) and grown to confluence (2–5 d). For the biotinylation experiments, cells were plated onto filters (Falcon HD Cell Culture Inserts, six-well format, 0.4-μm pore size; Becton Dickinson Labware, Franklin Lakes, NJ) at a density of ∼1 × 10⁶ cells. Where indicated, 5′ NT expression was enhanced by overnight incubation in medium containing 10 mM sodium butyrate before an experiment.

A hybridoma producing the mouse monoclonal IgG antibody 5NT4-2 (Siddle et al., 1981) was the generous gift of Dr. P. Luzio. This antibody inhibits 5′ NT enzyme activity by a maximum of ∼50% (Siddle et al., 1981). Thus, although 5′ NT is thought to form a dimer (Zimmermann, 1992) we expect this antibody to bind only one monomer per dimer. 5NT4-2 IgG was purified from ascites using E-Z-Sep (Pharmacia Biotech Inc., Piscataway, NJ) or from hybridoma supernatant using a protein A–Sepharose column. Monovalent antibody fragments (Fab) were prepared from IgG using published methods (Matko and Edidin, 1997). The final Fab fraction was incubated with protein A–Sepharose to remove any remaining IgG. Bisfunctional succinimidyl ester derivatives of the cyanine dyes Cy3 and Cy5 (Southwick et al., 1990; Mujumdar et al., 1993) were conjugated to purified Fab and IgG as per the manufacturer's instructions (Fluorolink Reactive Dye; Amersham Life Science, Inc., Arlington Heights, IL). The conjugation reaction was stopped by passing it over a column (10DG column; BioRad Laboratories, Hercules, CA) to separate the conjugated proteins from the unbound dye. The final dye/protein values were 2.9 and 1.7 for the Cy3 and Cy5 IgG conjugates, and 6.3 and 4.1 for the Cy3 and Cy5 Fab conjugates, respectively.

The GPI-anchorage of 5′ NT in the transfected MDCK clones was confirmed by phospholipase C treatment of Triton X-114 cell extracts (Hannan and Edidin, 1996) using precondensed Triton X-114 (Bordier, 1981). 5′ NT was immunoprecipitated from Triton X-114 enriched and depleted phases, subjected to SDS-PAGE, transferred to a Western blot, and detected by enhanced chemiluminescence (ECL; Amersham Life Science, Inc.).

Surface-specific biotinylation (Weisz et al., 1992) was performed on cells grown on filters. 5′ NT expression was enhanced by overnight incubation in medium containing 10 mM sodium butyrate. Before the experiment, the tightness of the monolayers was tested by assaying for leakage to the basolateral compartment of [³H]inulin added to the apical compartment. Immunoprecipitated, biotinylated 5′ NT was subjected to SDS-PAGE, transferred to a Western blot, and detected by enhanced chemiluminescence. The blots were quantified by densitometry. Polarity of surface biotinylated 5′ NT expression was determined as apical/(apical + basolateral).

Cells on coverslips were labeled for 15 min at 4°C with 100 μl of a mixture of donor (Cy3)- and acceptor (Cy5)-labeled antibodies. In all experiments, the antibodies were diluted in PBS supplemented with 0.9 mM CaCl₂, 0.52 mM MgCl₂, and 0.16 mM MgSO₄ (PBS⁺⁺) containing 1% BSA. The cells were rinsed twice for 5 min in PBS⁺⁺ at 4°C. The cells were then fixed for 30 min at room temperature in 4% formaldehyde in PBS⁺⁺, freshly prepared from a 16% formaldehyde solution (Electron Microscopy Sciences, Ft. Washington, PA). Finally, the coverslips were mounted on slides in PBS, with 50-μm-thick pieces of tape used to hold the coverslips away from the slide, and then sealed with nail polish. Note that we chose to fix the cells before the microscopy measurements to prevent potential reorganization of the proteins during the course of the experiments. To this point, in experiments where the cells were labeled with fluorophore-conjugated primary antibodies (IgG) and then shifted to 37°C for 30 min, the label appeared more “patchy” than in controls that had been immediately fixed.

Unless otherwise indicated, the concentration of Cy3-conjugated antibody was held constant at 50 μg/ml in each mixture, and Cy5-conjugated antibody was added to give the indicated molar ratio of donor to acceptor (D:A). In a control experiments, the saturating antibody concentration was determined to be ∼200 μg/ml. Thus in the FRET experiments, the total antibody concentration ranged from subsaturating to saturating. The experimentally measured ratio of donor to acceptor fluorescence was directly proportional to D:A applied to the cells.

In experiments measuring FRET between primary and secondary antibodies, cells were labeled with 50 μg/ml of Cy3-5NT4-2 IgG as above, washed twice in PBS⁺⁺ for 5 min at 4°C, incubated for 15 min at 4°C with either 5 or 50 μg/ml of Cy5-labeled secondary antibody (donkey anti– mouse H + L, dye/protein ratio ∼1.6; Jackson ImmunoResearch Laboratories, West Grove, PA), washed again, and then immediately fixed. The amount of Cy5 secondary antibody that bound increased only about twofold based on its relative fluorescence intensity, despite the 10-fold difference in concentration.

When secondary antibody was used to cross-link labeled 5′ NT, cells were labeled with the indicated D:A of 5NT4-2 IgG as above and then washed twice with PBS⁺⁺ for 5 min at 4°C. The cells were then incubated for 15 min at 4°C in the presence or absence of 10 μg/ml unlabeled secondary antibody (donkey anti–mouse H + L; Jackson ImmunoResearch Laboratories). After washing as before, the cells labeled without secondary antibody were fixed immediately. The cells labeled in the presence of secondary antibody were either fixed immediately or were incubated at 37°C for 15 min before fixation.

In the detergent extraction experiments, cells were labeled for 15 min at 4°C with 1:1 D:A of 5NT4-2 IgG, followed by a 30-min incubation at 4°C in either PBS⁺⁺ or PBS⁺⁺ containing 1% Triton X-100. The cells were then rinsed briefly with cold PBS⁺⁺ and fixed in 4% formaldehyde as above.

Cells were imaged on a fluorescence microscope (model Axiovert 135TV; Carl Zeiss, Inc., Thornwood, NY) using a 1.4 NA 63× Zeiss Plan-apochromat objective or a 1.3 NA 100× Zeiss Plan-neofluor objective. Digital images were collected using the IC300 digital imaging system (Inovision, Research Triangle Park, NC). Cy3 and Cy5 were detected using appropriate filter sets (Cy3 filter cube: excitation 515–560 nm, 565-nm long pass dichroic, emission 573–648 nm; Cy5 filter cube: excitation 590–650 nm, 660-nm long pass dichroic, emission 663–738 nm) (Chroma Technology Corporation, Brattleboro, VT). Images were collected with a Series 200 cooled CCD camera with a 1,340 × 1,037-pixel ICAF-1400 chip (Photometrics, Tucson, AZ). Fluorescence was excited with a 75-W xenon arc lamp. Image acquisition time was adjusted to maximize the range of CCD. Using typical exposure times for image acquisition (less than 5 s), no fluorescence was observed from a Cy3-labeled specimen using the Cy5 filters, nor was Cy5 fluorescence detected using the Cy3 filter sets.

FRET is widely used as a spectroscopic tool for detecting molecular interactions and molecular proximity in solution, as well as in membranes. It involves the nonradiative transfer of energy from the excited state of a donor molecule to an appropriate acceptor (Wu and Brand, 1994; Clegg, 1995, 1996).

The rate of energy transfer is inversely proportional to the sixth power of the distance, r, between the donor and acceptor. The efficiency of energy transfer E is defined with respect to r and R_o, the characteristic Förster distance for the donor and acceptor pair by

For example, when r = R_o, E is 50%, and when r = 2R_o, E is 1.5%. The value of R_o depends on the relative orientation of the donor and acceptor, the overlap interval between the emission spectrum of the donor and the excitation spectrum of the acceptor, and the fluorescence quantum yield of the donor. In our experiments, Cy3 was used as a donor, and Cy5 as an acceptor. R_o for this donor and acceptor pair has been calculated as 50 Å (Bastiaens and Jovin, 1996), assuming an orientation factor, κ², of 2/3 (Dale et al., 1979). For this value of R_o, when r = 50 Å, E is 50%, and when r = 100 Å, E is 1.5%.

Experimentally, FRET can be detected in several ways. Energy transfer causes quenching of donor fluorescence and sensitized fluorescence of the acceptor. It also reduces the donor lifetime and decreases the rate of irreversible photobleaching of the donor (Clegg, 1995, 1996). Imaging FRET techniques have been developed to measure all of these events. Methods described to date to measure energy transfer follow donor photobleaching (Kubitscheck et al., 1991, 1993; Hannan et al., 1993; Damjanovich et al., 1995; Gadella and Jovin, 1995; Jurgens et al., 1996), variations on sensitized acceptor fluorescence (Uster and Pagano, 1986; Adams et al., 1991; Bacskai et al., 1993; Kam et al., 1995), donor quenching (Kindzelskii et al., 1994; Xue et al., 1994; Bastiaens and Jovin, 1996; Bastiaens et al., 1996; Kindzelskii et al., 1996), and donor lifetimes (Oida et al., 1993).

In the present study, FRET was measured using a method developed for a laser confocal microscope (Bastiaens and Jovin, 1996; Bastiaens et al., 1996) modified by us for use with a conventional arc lamp microscope (Kenworthy and Edidin, 1997). In this method, samples are labeled with a mixture of donor- and acceptor-conjugated antibodies, and energy transfer is detected as an increase in donor fluorescence (dequenching) after complete photobleaching of the acceptor fluorophore. An advantage of this method is that all the parameters needed to quantitate E can be obtained from the same field of cells, eliminating the need to correct for differences in the amount of donor antibody bound in samples separately labeled with donor and acceptor (or only with donor) or to determine spectral correction factors necessary to quantitate sensitized acceptor fluorescence measurements (Jovin and Arndt-Jovin, 1989a,b). The validity of using donor dequenching to quantify FRET depends on the fact that the only factor that can lead to a difference in donor fluorescence in the presence and absence of acceptor is energy transfer.

To quantitatively measure E with this method, the acceptor must be sufficiently photolabile that it can be completely bleached, and the donor fluorescence must not fade significantly while images are acquired in the presence and absence of the acceptor. Cells labeled with Cy5-conjugated IgG were used to determine the minimum time required to completely bleach the Cy5. Typically, Cy5 was completely photobleached by 7 min or less of continuous arc lamp excitation using a Cy5 filter set and an additional 570-nm long pass filter in the excitation path. Under these conditions, greater than 97% of the Cy5 was bleached, and no Cy3 was bleached in control samples labeled with Cy3 IgG only. (In the absence of the long pass filter, a small amount of Cy3 was bleached during Cy5 bleaching.) This shows that Cy3 is stable enough to allow quantitative comparisons of donor fluorescence before and after acceptor photobleaching. Note that in these experiments, the Cy5 was bleached from an entire field of cells.

To perform an imaging FRET experiment, samples were labeled with both Cy3- and Cy5-conjugated antibodies in the indicated molar ratios, as described above. An initial image of Cy3 fluorescence (in the presence of the Cy5-conjugated antibodies) was obtained using Cy3 filter set. An image of Cy5 fluorescence was obtained using the Cy5 filter set and an additional 570-nm long pass filter in the excitation path, and then the sample was continuously illuminated for 7 min. An image of Cy5 fluorescence after photobleaching (<3% of the initial intensity) was then obtained, the long pass filter was removed, and another Cy3 fluorescence image was collected using the Cy3 filter set. Data were collected for four to five different fields from a single coverslip. The fluorescence intensities are reported in arbitrary units and are comparable within a given experiment, but they cannot be compared directly between experiments.

Images mapping FRET between labeled 5′ NT molecules were calculated from the increase in donor fluorescence after acceptor photodestruction by

after subtracting the dark current contribution and correcting the registration of the images using the Isee Pratt Index registration algorithm. The scaling factor of 10,000 was used to expand E (which scales from 0–1) to the scale of the 12-bit images (0–4,096). A value of 4,096 thus corresponds to E of 0.4096, or 40.96%. For cells labeled with donor only (D:A = 1:0), no significant energy transfer was observed (E < 2–3%).

The energy transfer efficiency images can potentially be analyzed on a pixel-by-pixel basis. However, because cell-to-cell variations in E contain information about the distribution of 5′ NT (see below), for further analysis we averaged over 40 × 40-pixel regions of interest (17.64 μm² at 63×, or 6.97 μm² at 100×) chosen from cells that were in focus. One region of interest was chosen per cell, and these areas were chosen so that they avoided the edges of the cells, where artifacts in the energy transfer efficiency images sometimes occurred. The mean fluorescence intensities and E were calculated for identical regions of interest for the registered Cy3 prebleach, Cy5 prebleach, Cy3 postbleach, and E images. Between 10 and 30 regions of interest were chosen from each field of cells, such that cells covering the complete range of 5′ NT expression levels were sampled. In experiments where clustering of 5′ NT was induced by secondary antibody, data were also collected with 5 × 5-pixel square regions of interest for areas on cells that were either depleted of 5′ NT or enriched in clusters. Because of the small sampling size, these data were more noisy and were scattered around the average E obtained using 40 × 40-pixel sample areas (data not shown).

Beads binding known numbers of IgGs (“Quantum Simply Cellular Beads,” Flow Cytometry Standards Corporation, San Juan, Puerto Rico) were labeled with saturating concentrations of the same antibodies used to label the cells at room temperature for 1 h, washed twice in PBS, and then mounted under a coverslip in PBS. The saturating antibody concentration was titrated for Cy3-conjugated antibody by flow cytometry, and the same concentration was then used to label the Cy5 beads. The fluorescence intensity of beads was measured by collecting images while focusing at the maximum apparent diameter of the bead or above and then summing the intensity within a circular region of interest that just included the entire bead. (Control experiments established that the integrated fluorescence intensity associated with a bead was essentially constant for focal planes ranging from the top to the center [maximum apparent diameter] of the bead.) We then generated a calibration curve of total fluorescence intensity for a given number of acceptor-labeled antibodies. Using this, we calculated the number of acceptor-bound antibodies on the cells. Several assumptions were made to perform this calculation. First, we assumed that one monoclonal antibody binds one protein on the cell surface. Second, it was assumed that all the fluorophores bound to the bead contributed to the observed fluorescence intensity. This could underestimate the average fluorescence per fluorophore if the beads are not completely transparent. Third, the surface area of the apical plasma membrane was assumed to correspond to its projected area in the image. This would tend to underestimate this area because it ignores surface details such as microvilli.

5′ NT was expressed predominantly on the apical membrane of transfected MDCK cells. When living cells expressing 5′ NT were labeled with a fluorophore-conjugated monoclonal antibody and then fixed before imaging, fluorescence was distributed uniformly across most of the apical membrane and concentrated in punctate structures, likely microvilli (see Fig. 1). In cells grown on filters, fixed, and labeled from the basolateral surface, a small amount of basolateral fluorescence was apparent (data not shown). The polarity of 5′ NT surface expression was 73.3 ± 0.1% (n = 3) apical based on domain-specific biotinylation of cells in which 5′ NT expression was induced before the experiment. This predominantly but not exclusively apical polarization is similar to the polarity of 5′ NT in human intestinal epithelial cells (Strohmeier et al., 1997). The cell-to-cell variation in the expression of 5′ NT is typical of transfected MDCK cells (Lisanti et al., 1989). That 5′ NT was GPI-anchored in the transfected cells was confirmed in cell extracts, where 5′ NT shifted from a Triton X-114 detergent–enriched phase to an aqueous phase after phosphatidylinositol-specific phospholipase C treatment (data not shown).

In experiments that follow, we use FRET to determine the membrane distribution of the GPI-anchored protein 5′ NT. We do this by testing properties of the observed FRET against predictions for FRET based on the theory in the  Appendix, summarized in Table I. First, we measure the dependence of energy transfer on donor and acceptor surface density and D:A for cells expressing a wide range of 5′ NT surface densities, using both monovalent and bivalent antibodies as probes. Second, we estimate the absolute surface density of acceptor-labeled 5′ NT so that we can directly compare our data to theoretical curves. Finally, we measure energy transfer for molecules known to “cluster,” primary and secondary antibodies, and for two different conditions previously shown to induce clustering of GPI-anchored proteins, cross-linking with secondary antibodies, and detergent extraction.

We measured FRET in terms of dequenching of donor fluorescence after complete photobleaching of the acceptor fluorophore. Data from a typical imaging FRET experiment are shown in Fig. 1. The initial donor (Cy3) image represents donor fluorescence in the presence of acceptor, Cy5 (Fig. 1,a). As expected, the Cy5 image collected before photobleaching (Fig. 1,b) was identical to the Cy3 image since the same antibody was used for both the donor and acceptor label. After completely bleaching acceptor (Cy5) (Fig. 1,d), a second donor (Cy3) image was collected (Fig. 1,c). The fluorescence of the donor (Cy3) in some of the cells increased (Fig. 1, a and c, arrows), while in other cells, there was little to no change in donor fluorescence (Fig. 1, a and c, arrowheads). Increased donor fluorescence after destruction of the acceptor indicated that donor fluorescence was quenched in the presence of the acceptor because of energy transfer. In general, the largest dequenching was observed in cells expressing the highest amounts of protein.

Images of E were calculated from the donor images obtained before and after acceptor photodestruction, using Eq. 2. The calculated E image for the data of Fig. 1 is shown in Fig. 2,a. There was significant energy transfer between labeled 5′ NT molecules. As shown in Fig. 2 a, E varied substantially from cell to cell, in this experiment from 10% to over 30%, and was high in cells expressing high amounts of 5′ NT at the apical plasma membrane.

The cell-to-cell variation in E contains information about the distribution of 5′ NT molecules on the cell surface (see Table I, test 3). To obtain this information, we sampled the average values of E, acceptor fluorescence intensity, and donor fluorescence intensity after acceptor photodestruction, from 40 × 40-pixel square regions of interest on individual cells (Fig. 1,c, box). This area represented ∼1/5 at 63× or 1/15 at 100× of the projected surface area of a cell of ∼100 μm². The relationship between E and acceptor fluorescence for the cells shown in Fig. 1 is shown graphically in Fig. 2,b. Each datum represents the mean E and acceptor fluorescence taken from one of the cells in the field. Since the acceptor fluorescence (though reported in arbitrary units) is proportional to the relative surface density (number of proteins per unit area) of 5′ NT, Fig. 2 b shows that E increased as a function of increasing surface density of 5′ NT molecules.

Depending on the distribution of donor- and acceptor- labeled molecules, E may depend on the surface density of donor and/or acceptors, the extent of labeling, and D:A (Table I and  Appendix). In our experiments, the surface density of 5′ NT varied from cell to cell because the cells differed in their expression of the protein (Fig. 1). The surface density of donors and acceptors could be changed by varying D:A, the ratio of donor- and acceptor-labeled antibodies used to label the cells. We expected that for 5′ NT randomly distributed on the cell surface, energy transfer between labeled 5′ NT would scale with the surface density of acceptor, regardless of the way in which the surface density of acceptor was varied. That is, we expect similar values of energy transfer for cells with a high surface density of 5′ NT but labeled with a low concentration of acceptor-conjugated antibody, and for cells with a low surface density of 5′ NT but labeled with a high concentration of acceptor antibody, as long as the acceptor surface density is the same in each cell group of cells (Table I, Fig. 1, 2). Energy transfer was not expected to scale with surface density if 5′ NT was exclusively distributed in clusters (Table I).

Fig. 3 shows the experimental dependence of E on D:A, donor surface density, and acceptor surface density. When cells were labeled with a constant molar concentration of donor-labeled IgG, with increasing concentrations of acceptor-labeled IgG to give D:A ranging from 1:0.5 to 1:5. It can be seen that for a single D:A, energy transfer increased with increasing 5′ NT surface density, measured in terms of either donor (Fig. 3,a) or acceptor (Fig. 3,b) fluorescence, and went to zero in the limit of low surface densities. This dependence of E on surface density is inconsistent with a model in which all surface 5′ NT is in clusters (Table I).

For a given donor surface density (Fig. 3,a), E increased as D:A increased from 1:0.5 to 1:5. This is apparent in the bifurcation of the data curves in Fig. 3,a. In contrast, for a given acceptor surface density (Fig. 3,b), E was approximately the same at all the D:A examined. We also note that the shape of the experimental curves was similar to that predicted for randomly distributed molecules (Fig. 2), although they cannot be directly compared here because the acceptor surface density and r are not known (see below for an estimate).

The strong dependence of E on the acceptor surface density, but not donor surface density, is consistent with the theoretical prediction for donors and acceptors randomly distributed in the plane of the membrane (Fig. 2). However, this independence of E on donor surface density only holds in the limit where there are few donors in the excited state compared with the number of acceptors present (Fung and Stryer, 1978). Consistent with this, we found that if cells were labeled with a constant concentration of acceptor (50 μg/ml) and varying amounts of donor to yield the indicated D:A, energy transfer actually decreased as the concentration of donor was increased to yield D:A of 5:1 (Fig. 3,c). For samples labeled with low concentrations of donor (D:A of 0.5:1 and 1:1), the data were similar to those described above (Fig. 3 b). Therefore, in all our experiments, samples for FRET were labeled with a constant low concentration of donor (50 μg/ ml) and varying concentrations of acceptor.

We considered the possibility that the bivalent IgG used to label 5′ NT may disrupt its normal membrane distribution. To test this, we repeated the experiments in Fig. 3, a and b, using cells labeled with a monovalent Fab. Fig. 4 shows the results of such an experiment. As above, cells were labeled with a constant amount of donor and with increasing amounts of acceptor. The pattern of immunofluorescence labeling was similar for cells labeled with IgG and Fab (data not shown). As we had observed for the IgG-labeled samples, E as a function of acceptor surface density was approximately the same for all D:A (Fig. 4 b). However for the Fab-labeled samples, a small but systematic increase in E was observed with increasing concentrations of acceptor. In an experiment where we directly compared the magnitude of E at a given acceptor fluorescence intensity for samples labeled with IgG versus Fab, we found that E was higher for the Fab-labeled samples (data not shown). This is most likely due to differences in the dye/protein ratio for the acceptor-labeled molecules (4.1 for Fab vs 1.7 for IgG), but it could also be due to differences in the size and/or the relative flexibility of Fab and IgG (Kam et al., 1995; Matko and Edidin, 1997). These factors may also account for the increase in E with increasing concentration of acceptor-Fab.

We also made FRET measurements in cells that had not been incubated with butyrate, but which nevertheless displayed detectable amounts of 5′ NT. These experiments were done for two reasons. First, we wanted to further test the dependence of E on 5′ NT surface density to see whether E extrapolated to zero at low surface densities (Table I). Second, the butyrate treatment used to induce high expression of 5′ NT could create artifacts because of overexpression of the protein. For instance, the enrichment of 5′ NT in microdomains in butyrate-treated cells may be limited by the availability of other components of the putative microdomains. Consistent with the lower surface densities of 5′ NT, we found that E was correspondingly lower on the untreated cells (data not shown and Figs. 6 and 7). As we had found for the butyrate-treated cells, at a given acceptor surface density E was similar at all D:A examined (data not shown). This suggests that the distribution of 5′ NT is not affected by the level of expression of the protein.

In the experiments described above, the acceptor surface densities were presented in arbitrary units; hence, we could not directly compare the experimental data with theoretical predictions. To compare experimental data with theoretical predictions, we estimated absolute surface densities of acceptors on cell membranes from the measured fluorescence intensities using a set of calibration standards, 8-μm-diam beads with known antibody binding capacities. Fig. 5 compares the experimental values of E plotted as a function of absolute acceptor surface density (Fig. 5,a), with the theoretical values of E for randomly distributed donors and acceptors (Fig. 5,b). We estimated maximum acceptor surface densities of 20,000 per μm² (Fig. 5,a). These values are high and may be overestimates, but they are not unprecedented (Rothberg et al., 1990; Hille, 1992). The theoretical curves (Fig. 5 b) were calculated for values of closest approach, r, ranging from r = 0, where the donor and acceptor are in physical contact, to r = 2R_o, where the closest possible approach of the donor and acceptor is constrained to 100 Å. If r is approximated by the diameter of the donor- and acceptor-labeled molecules (Zimet et al., 1995), r = 1.5R_o would be roughly comparable to the size of an Fab, which has been estimated as a cylinder with a diameter of 80 Å and a height of 70 Å (Kubitscheck et al., 1993).

A comparison of Fig. 5, a and b, shows that the overall shapes of the experimental and theoretical curves are similar, and that the experimental data fall within the range of the theoretical predictions. The experimental data are similar to the theoretical curves for r = 0 at low surface densities, and r = 1.5R_o at high surface densities. Though this variation in r as a function of surface density may reflect the biology of 5′ NT, it may also result from errors in the estimate of the acceptor surface density and from the fact that the theoretical calculations assume one fluorophore per protein molecules, while our Fab and IgG labels carry two or more fluorophores per molecule.

As a direct test of whether our method could detect clustered molecules, we measured energy transfer from donor-labeled anti–5′ NT Ig to acceptor-labeled anti-Ig antibodies. Direct binding of the secondary antibodies to the primary antibodies should lead to relatively high values of E, and E should reflect the combined contributions of “clustered” (directly bound) and randomly distributed molecules ( Appendix). We expect that this system should behave as a mixture of randomly distributed and clustered molecules, where f_clustered is constant (Table I, Fig. A3, a and b). Although at first it might appear that since the acceptors bind donors that this should instead be equivalent to the model presented in Fig. 3 c, this is not the case because in our experiment, the ratio of primary and secondary antibodies bound to any given cell, and thus f_clustered, is constant.

As expected, for samples labeled with donor-conjugated primary and acceptor-conjugated secondary antibodies, the amount of secondary antibody bound to any given cell was directly proportional to the amount of primary antibody bound, and thus proportional to the surface density of 5′ NT (data not shown). Compared with a control sample labeled with donor- and acceptor-conjugated primary antibodies, significantly higher values of E were observed for the samples labeled with the donor-conjugated primary and acceptor-conjugated secondary antibodies (Fig. 6). Moreover, in the clustered samples, E increased as the concentration of acceptor-conjugated secondary antibody used to label the cells was increased. In this experiment, E increased from a maximum of ∼20% to a maximum of close to 40%, as D:A was increased from a nominal ratio of 1:0.1 to 1:1. For comparison, an E of 28% has been measured between the A- and B-subunits of the intact structure of cholera toxin, molecules in molecular contact (Bastiaens et al., 1996).

The increase in E observed as the concentration of acceptor in D:A was increased could reflect an increase in the fraction of donors to which acceptors were bound (f_clustered in Eq. A5), an increase in the number of acceptors (secondary antibodies) bound per donor (E_clustered in Eq. A5), or both. E for the clustered molecules also showed some dependence on the acceptor surface density. This is probably due to intercluster energy transfer. Note especially that at the lowest surface densities observed, E for the control sample was less than 5%, compared with >10% or >20% for the samples labeled with 5 or 50 μg/ml of acceptor- labeled secondary antibody, respectively.

GPI-anchored proteins on cell surface can be clustered by cross-linking with secondary antibody (Mayor et al., 1994; Fujimoto, 1996) or by detergent extraction of cells (Mayor and Maxfield, 1995). If this clustering also occurs over molecular length scales, it ought to cause a detectable change in the energy transfer between labeled 5′ NT molecules.

To cluster 5′ NT with secondary antibody, cells were labeled with donor- and acceptor-conjugated antibody followed by an anti-IgG secondary antibody and a brief incubation at 37°C. With this treatment, the label clustered into large punctate structures (Fig. 7,c). For a given acceptor surface density, higher values of E were observed in cells labeled with secondary antibody than in control cells (Fig. 7,e). This difference was not very large, in part because, for the clustered sample, E is an average for the areas depleted and enriched in 5′ NT (Fig. 7 d). This finding is consistent with a report that the average E for cells labeled with donor- and acceptor-labeled Concanavalin A was similar under conditions where the label was ring-stained and when it was patched (Dale et al., 1981).

5′ NT is found in low-density, detergent-insoluble membrane microdomains in intestinal epithelial cells (Strohmeier et al., 1997) and rat lung endothelial cells (Schnitzer et al., 1995). To see if Triton X-100 extraction changed the organization of 5′ NT in intact MDCK cell membranes, living cells were labeled at 4°C with donor- and acceptor-labeled antibodies and then incubated on ice with 1% Triton X-100 for 30 min before fixation. As reported for other GPI-anchored proteins (Mayor and Maxfield, 1995), 5′ NT was not significantly solubilized under these conditions, since the intensity and pattern of its labeling were very similar to control cells (Fig. 8). However, in some cells, dark unlabeled regions in the membrane (presumably holes) were apparent, indicating that other membrane components had been solubilized (Fig. 8,c, arrow). E measured after detergent extraction was systematically higher than controls, consistent with a shift to a partially clustered distribution of 5′ NT after detergent extraction (Fig. 8 e).

These results suggest that not all 5′ NT was clustered after secondary antibody labeling or detergent extraction, but instead was present as a mixture of randomly distributed and clustered molecules. To this point, it is important to note that changes (or lack thereof) in the apparent organization of the protein at the light or even the electron microscopic level may not be directly correlated with changes detected by FRET, since they measure distances over different length scales (c.f., Damjanovich et al., 1995).

Membrane microdomains enriched in GPI-anchored proteins, GSL, and cholesterol have been operationally defined in terms of detergent-insoluble, low-density membrane fractions; however, these microdomains have not been detected by other techniques (for review see Harder and Simons, 1997). In the present study, we used imaging FRET, a method that increases the resolution of immunofluorescence microscopy to the molecular scale, to probe for microdomains enriched in a GPI-anchored protein in the apical plasma membrane of MDCK cells. We expected that if most of the GPI-anchored protein 5′ NT was in membrane microdomains, then we would be able to detect FRET between 5′ NT molecules that was consistent with clustering (Table I).

Using imaging FRET, we obtained images that showed significant cell-to-cell variation in efficiencies of energy transfer between labeled 5′ NT molecules. E strongly correlated with the surface density of 5′ NT and approached zero at low surface densities (Figs. 3–6). These observations suggest that most of 5′ NT is not in clusters at the apical membrane of MDCK cells; if it were, we would have expected to measure high E even at low surface densities (Table I). These observations were not due to the failure of the method to detect clusters since we detected clustered donors and acceptors in a simple model system, secondary antibodies bound to primary antibodies (Fig. 6).

The distinct dependence of E on the surface density of 5′ NT (Figs. 3–6) is consistent with either an entirely random distribution of the protein or a mixture of randomly distributed and clustered 5′ NT (Table I). If some 5′ NT is in clusters and some is randomly distributed, we expect that E will not necessarily go to zero in the limit of low surface densities, and E will be sensitive to D:A (Table I). If little or no 5′ NT is in clusters, then we expect E to go to zero in the limit of low surface density to be insensitive to D:A.

We found that E approached zero in the limit of low 5′ NT surface densities (Figs. 3–6), and the shape of the experimental curves was similar to that predicted theoretically for a random distribution (Fig. 5). E depended strongly on the surface density of acceptor, and not of the surface density of donors for relatively low concentrations of the donor fluorophore. Regardless of D:A, data from an individual experiment tended to fall on a single curve when plotted as a function of acceptor surface density in cells expressing widely varying concentrations of protein (Fig. 3). However, in some experiments (Fig. 4) we observed small shifts in E for samples labeled with different D:A ratios, which hints that some clusters may be present. We thus cannot completely rule out the possibility that though most are randomly distributed, some 5′ NT molecules are clustered. We expect that under some circumstances, FRET for mixtures of randomly distributed and clustered molecules will appear similar to FRET for a purely random distribution, particularly in the limit where f_clustered and/or E_clustered is small, and f_random and/or E_random is large (see  Appendix). This could explain for instance why we did not observe a larger effect on E in cells where we induced clustering of GPI-anchored proteins by secondary antibody-induced cross-linking, or by detergent extraction of intact cells (Figs. 7 and 8). We calculated that if 10% of the molecules were clustered, data for a mixed population would appear very similar to a pure random distribution (assuming r = R_o). However, large differences are expected when f_clustered = 50% (see  Appendix). Based on these observations, the simplest interpretation of our data is that 5′ NT is predominantly randomly distributed under the conditions of our experiments.

It is important to emphasize that our conclusion that 5′ NT is predominantly randomly distributed depends on the presence of FRET and not its absence. In a previous study from our laboratory, no FRET was detected between labeled gD1-DAF molecules under steady-state condition, implying that gD1-DAF was dispersed, i.e., randomly distributed (Hannan et al., 1993). However, the absence of FRET does not necessarily eliminate the possibility that molecules are clustered together, since among other possibilities the distance separating them in the cluster may be larger than can be detected by FRET. In the present study we were able to detect FRET between labeled 5′ NT molecules; this indicates that, on average, the proteins are already within 10's of Å of one another. This provides further evidence that FRET would be able to detect enrichment of 5′ NT in microdomains, i.e., lipid rafts. Reexamination of the lateral organization of gD1-DAF using our current FRET method shows that energy transfer is detected between labeled gD1-DAF molecules under steady-state conditions and is correlated with protein surface density, similar to our results for 5′ NT (Nguyen, T., A. Kenworthy, and M. Edidin, unpublished observations). The difference between our past and present results may be due to lower concentrations (surface densities) of labeling antibodies in our previous experiments, and the sensitivity of the current method to cell-to-cell variations in E. This further emphasizes the most important advantage of imaging FRET over nonimaging FRET experiments, which typically yield average E values for a population of cells (Hannan et al., 1993; Matko and Edidin, 1997): imaging FRET generates images mapping energy transfer efficiencies. Although in the current study we have focused on protein homoassociations, imaging FRET is also uniquely suited for performing “imaging biochemistry” of protein– protein and protein–lipid heterointeractions in intact cells.

To further verify our conclusion that most 5′ NT is randomly distributed in the cell surface would require a quantitative comparison of our data with the theoretical predictions. Variations on the analytical approach we applied here have been used to quantitatively interpret FRET data in a variety of membrane systems (e.g., Holowka and Baird, 1983a,b; Dewey and Datta, 1989; John and Jähnig, 1991; also see Mátyus, 1992 and Clegg, 1996 for a more comprehensive list). However, our ability to extend our current analysis from a qualitative to a quantitative one is limited by several factors. First, there is some spread in the energy transfer versus acceptor surface density curves that could mask differences in the data sets. Factors contributing to this variability include inhomogeneities in the excitation across the field of view, small local variations in quenching of donor, and the inherent heterogeneity of fluorescence labeling pattern of the cell surface due to the presence of microvilli and the curvature of the apical membrane itself. Second, the lower limit of detectability of FRET with our method is conservatively 5%, although in many experiments we measured apparent E for negative controls (labeled with donor only) of as low as 2–3% (Fig. 4). This could be further improved by additional background subtraction. In the current experiments, because we were imaging confluent monolayers of cells, the only background subtraction we included was for the so-called dark current, a constant contribution due to noise from the CCD camera. With higher sensitivity we could estimate the extrapolation of E and the acceptor surface density to zero with greater confidence. Third, there are limits to our comparisons of experimental results to theory and with the theoretical calculations themselves. Our ability to rigorously test the theoretical predictions would be improved by better estimates of acceptor surface density and r. A physically based approximation of r, for instance, would require more detailed structural information about 5′ NT, including the position of the epitope and the orientation of the bound antibody. To this point, we note that a number of sophisticated analyses have been developed that incorporated detailed information about the experimental system, such as the position of the donor fluorophore on the molecule of interest (e.g., Zimet et al., 1995). This kind of information could be usefully applied in the analysis of imaging FRET data for better characterized experimental systems. The analysis would also be improved by better theoretical models for mixed populations, including specific cross-terms between the randomly distributed and clustered molecules.

It is well known that the distribution of GPI-anchored proteins in cell membranes is sensitive to fixation and labeling conditions. For example, GPI-anchored folate receptor was reported to be clustered (Rothberg et al., 1990), but this was subsequently shown to be induced by cross-linking of secondary antibodies (Mayor et al., 1994). Clustering of 5′ NT itself has also been shown after antibody cross-linking (Howell et al., 1987). In our experiments, we observed very similar, dispersed labeling patterns produced by either monovalent Fab or bivalent IgG when the cells were directly fixed after labeling. In addition, the organization of the primary antibodies became more punctate (clustered) in the presence of secondary antibodies (Fig. 7 and data not shown). Thus, our results are similar to previous reports in this regard (Rothberg et al., 1990; Mayor et al., 1994). However, very recent work suggests that certain fixation conditions may act to disperse preexisting clusters of the folate receptor (Wu et al., 1997), reopening the question of how to best stabilize the native distribution of GPI-anchored proteins. This issue will require further study. Nevertheless, our current results are consistent with reports (Parton et al., 1994; Mayor and Maxfield, 1995; Fujimoto, 1996; Rijnboutt et al., 1996) of predominantly random steady-state distributions of GPI-anchored proteins, measured at the level of resolution of the electron microscope. Compared with electron microscopy, imaging FRET has the advantages of higher labeling efficiency, a larger sample size, and most importantly, increased resolution, to the molecular level.

The first experimental evidence for the existence of membrane microdomains enriched in GPI-anchored proteins was the isolation, as buoyant complexes, of detergent-insoluble membrane fractions enriched in GPI- anchored proteins, GSL, and cholesterol from MDCK cells (Brown and Rose, 1992). The GPI-anchored protein PLAP was found to become detergent insoluble in the Golgi, a property that persisted even after the protein reached the apical membrane (Brown and Rose, 1992). Additional components of detergent-insoluble membrane microdomains were later shown to include signal-transducing lipid-modified proteins such as nonreceptor tyrosine kinases and the caveolar marker caveolin (Stefanova et al., 1991; Sargiacomo et al., 1993;Arreaza et al., 1994; Melkonian et al., 1995). Recently, a number of studies have helped clarify the relationship between membrane microdomains enriched in GPI-anchored proteins, detergent-insoluble complexes, and caveolae, 70–100-nm invaginations of the plasma membrane that are decorated with the protein caveolin (Fra et al., 1994; Schroeder et al., 1994; Gorodinsky and Harris, 1995; Mayor and Maxfield, 1995; Schnitzer et al., 1995, 1996; Smart et al., 1995; Hannan and Edidin, 1996; Ahmed et al., 1997). These studies indicate that proteins and lipids that share the common property of detergent insolubility are not necessarily associated in intact cell membranes, but leave open the question of the size and nature of the microdomains before detergent extraction (Kurzchalia et al., 1995; Edidin, 1997; Harder and Simons, 1997; Weimbs et al., 1997). There is clearly a need for a more precise definition of what constitutes a functional membrane microdomain in intact cell membranes.

Our findings, obtained using a high-resolution imaging technique, begin to place distinct limits on the structure of microdomains enriched in GPI-anchored proteins in intact cell membranes. We report here that the GPI-anchored protein 5′ NT, which is known to associate with detergent-insoluble complexes (Mescher et al., 1981; Schnitzer et al., 1995; Strohmeier et al., 1997), is also resistant to Triton X-100 extraction in MDCK cells. Yet it appears that most 5′ NT are randomly distributed and are not clustered over the <100-Å length scale of the FRET measurements. This places limits on the ways in which GPI-anchored proteins can associate with lipid rafts. For example, our data argue against a model where 5′ NT is predominantly associated with a finite number of rafts, since we would have expected to measure relatively high energy transfer because of clustering of the protein in rafts, even at low surface densities of 5′ NT expression (Fig. 3). The limitations of our current measurements prevent us from ruling out the possibility that FRET between 5′ NT arises from a mixture of a large fraction of randomly distributed and a small fraction of clustered (raft-associated) molecules. However, it is interesting to consider the consequence of a purely randomly distribution of 5′ NT for the structure of lipid rafts. If this were the case, then these membrane microdomains must either be vanishingly small (in agreement with a current model [Harder and Simons, 1997]), or alternately must comprise the entire apical membrane. Our results also have implications for the membrane organization of GPI-anchored proteins during membrane trafficking and sorting, since the biochemical properties of the membrane microdomains involved in sorting and the steady-state organization of GPI-anchored proteins are assumed to be similar. This could be further tested by directly examining the membrane organization of GPI- anchored proteins and other apically destined proteins and lipids in the Golgi. Further work will be also be required to determine whether functional associations of other lipid-modified proteins and GSL can be visualized in cell membranes, and whether these associations are mediated by lipid–lipid or protein–lipid interactions. Imaging FRET will be a powerful tool to further investigate these questions in intact cells.

We gratefully acknowledge Drs. T. Jovin, D. Arndt-Jovin, and P. Bastiaens (Max-Planck Institute for Biophysical Chemistry, Göttingen, Germany) for introducing us to the imaging FRET method described here. We thank members of the Edidin lab and Dr. A. Hubbard (Johns Hopkins Medical School, Baltimore, MD) and members of her laboratory for their ongoing support and interest in this study. We also thank two anonymous reviewers for a number of suggestions that improved the manuscript. Dr. Y. Ikehara (Fukuoka University School of Medicine, Fukuoka, Japan) and Dr. P. Luzio (University of Cambridge, Cambridge, England) generously provided the rat liver 5′ NT cDNA and the 5′ NT antibodies, respectively. The expert technical assistance of Mr. A. Nechkin, Mrs. T. Wei, and Mr. T. Du with image analysis, flow cytometry, and biotinylation experiments, respectively, is acknowledged. The FRET experiments were performed at the Advanced Microscopy Facility at the Department of Biology at Johns Hopkins University.

This work was supported by 5P01DK44375 from the National Institutes of Health to M. Edidin.

5′ NT

5′ nucleotidase

c_A

reduced acceptor surface density

c_D

reduced donor surface density

D:A

molar donor/acceptor ratio

E

energy transfer efficiency

E_clustered

theoretical energy transfer efficiency for clustered molecules

E_mixture

theoretical energy transfer efficiency for a mixture of randomly distributed and clustered molecules

E_random

theoretical energy transfer efficiency for randomly distributed molecules

f_A

mole fraction of acceptors

f_D

mole fraction of donors

f_U

mole fraction of unlabeled molecules

f_clustered

fraction of clustered molecules

f_random

fraction of randomly distributed molecules

Fab

monovalent antibody fragment

FRET

fluorescence resonance energy transfer

GPI

glycosylphosphatidylinositol

GSL

glycosphingolipids

FRET detects the proximity of donor- and acceptor-labeled molecules over distances of <100 Å (Eq. 1). FRET can be used to study the distribution of molecules in membranes because the average spacing between molecules of interest will depend primarily on their lateral distribution (Fig. A1). Molecules may be within FRET distance either because they are clustered or because they are randomly distributed at surface densities high enough so that there is a fraction of randomly distributed labeled molecules in FRET proximity. The basis for FRET can be determined by considering predictions of theoretical models for FRET between clustered or between randomly distributed molecules. Below we consider the predictions for three models of proteins labeled with a mixture of donor and acceptor fluorophores: randomly distributed molecules, entirely clustered molecules, and a mixture of randomly distributed and clustered molecules. We show that we can distinguish between the models by determining the dependence of E on the total surface density of the molecules of interest and the mole ratio of donor to acceptors (D:A) used to label them.

For randomly distributed donors and acceptors in membranes, the energy transfer efficiency E_random is a function of R_o, r, and the surface density of acceptors (Shaklai et al., 1977; Fung and Stryer, 1978; Wolber and Hudson, 1979; Dewey and Hammes, 1980; Snyder and Freire, 1982; Yguerabide, 1994). Here, r is defined as the distance of closest potential approach of the donors and acceptors. This takes into account the fact that donors and acceptors are attached to molecules, proteins or lipids, that have some finite size. A typical value of r for energy transfer between small lipid probes is ∼10 Å (Dewey and Hammes, 1980). For protein–protein interactions, r can be approximated by the protein diameter, for instance, ∼40 Å for calcium ATPase (Dewey and Datta, 1989; Zimet et al., 1995).

The equation relating E_random, r, R_o, and acceptor surface density is in a form that must be solved numerically, and thus a number of analytical approximations of this equation have been developed (Shaklai et al., 1977; Wolber and Hudson, 1979; Dewey and Hammes, 1980; Snyder and Freire, 1982; Yguerabide, 1994). Two approximations that together accurately span a useful range of values of r are from Dewey and Hammes (1980) and Wolber and Hudson (1979). The approximation of Wolber and Hudson (1979) is

where c_A is the so-called reduced acceptor surface density, a dimensionless parameter equal to R_o² multiplied by the acceptor surface density, and A_1,2 and k_1,2 are constants that are different for different values of r. Dewey and Hammes (1980) derived fractional approximations for E_random, the first of which is given by

Here again c_A is the reduced acceptor surface density, as defined above. Eq. A1 is valid for r < 1.3R_o and Eq. A2 is valid for r ≥ R_o. Other limiting conditions are: (a) The number of donors must be small enough that donor- donor transfer is negligible; (b) the number of donors in the excited state must be small compared with the number in the ground state so that donors do not compete for transfer to a given acceptor; (c) r must not change over the excited state lifetime of the donor; and (d) all donor–acceptor pairs must have the same R_o (Fung and Stryer, 1978; Wolber and Hudson, 1979; Zimet et al., 1995).

In Fig. A2, we plot Eqs. A1 and A2 as a function of acceptor surface density, for various values of r. E_random is dependent on r, reaching its highest potential value as r approaches zero. For any given value of r, E_random is zero in the limit of very low acceptor surface densities and increases monotonically with increasing acceptor surface density (Fig. A2). This is because as surface density increases, the distance between adjacent donor- and acceptor-labeled molecules decreases (Fig. A1, a and b). Although E_random is dependent on acceptor surface density, it is independent of donor surface density (Eqs. A1 and A2) since each donor experiences the same average acceptor surface density. (As indicated above, this is only true in the limit where the donor surface density is low enough that excited state donors do not compete for acceptors.) For example, if two samples with the same surface density of protein were labeled with different D:A (Fig. A1, b and c), E_random would be higher for the sample labeled with the higher concentration of acceptors (Fig. A1,c). Note also that since E_random is only sensitive to the surface density of acceptor-labeled molecules, the presence of unlabeled molecules does not influence E_random. Using this information, E_random can be estimated for the molecules in Fig. A1 by assigning a scale to the model. For example, if the particle diameter is set as 50 Å (r = R_o), then the acceptor surface density in Fig. A1 c is 2500/μm², yielding an E_random of 7% (Eq. A1).

A simple model has been derived to predict the energy transfer efficiency for clustered molecules, E_clustered, in the case where the clusters are small well-defined oligomers such as dimers and trimers (Veatch and Stryer, 1977; Adair and Engelman, 1994). This model makes several simplifying assumptions, including the assumption that there are no surface density–dependent interactions between oligomers, and that all of the molecules of interest are oligomerized. Thus, it also assumes that labeling the molecules does not affect their oligomerization. Under these conditions,

Here, n is the number of units in the oligomer, f_DU is the total mole fraction of donor-labeled and unlabeled molecules of interest, and E_oligomer is the energy transfer efficiency for the oligomer. For the case of dimers (n = 2), this simplifies to

where E_dimer is the energy transfer efficiency of a dimer labeled with one donor and one acceptor, and f_A is the mole fraction of acceptor-labeled molecules (f_A + f_D + f_U = 1). This model predicts that E_clustered will depend on both D:A and the extent of labeling of the molecules of interest. For example, for two samples with the same surface density of protein (Fig. A1, e and f), if we assume E_dimer = 50% and the indicated D:A, then E_clustered = (50%)(.25) = 12.5% for Fig. A1,e, while E_clustered = (50%)(0.75) = 37.5% for Fig. A1,f. The cluster model also predicts that E_clustered will be independent of the surface densities of the labeled molecules of interest. Thus, E_clustered = (50%)(.25) = 12.5% for two samples with different surface densities but labeled with the same D:A (Fig. A1, d and e). Based on this prediction, E_clustered would be expected to be nonzero even at low surface densities of the molecule of interest. These properties contrast with the predictions for randomly distributed molecules (Fig. A1, a–c), where E_random scales strictly with the acceptor surface density (Eqs. A1 and A2).

Although this model may be oversimplified, it provides a useful tool to think about how E_clustered depends on D:A, the extent of labeling, and both donor and acceptor surface density for molecules constrained to a clustered distribution. While the model presented above equates “clustered” molecules with “associated” molecules, this of course is not necessarily the case. In general, to predict E_clustered for more complex clustered distributions would require more specific information about the geometry of the clustered molecules such as the size and shape of the clusters, as well as the position of the fluorescent probe(s) on the molecules of interest. E_clustered would then ultimately depend on the probability of labeling adjacent members of an individual cluster within FRET distance of one another with donors and acceptors.

The simple model for clusters presented above assumes that all of the molecules of interest are associated in clusters. If a mixture of monomeric, randomly distributed molecules and clustered molecules is present, we would expect two contributions to E_mixture, one from the randomly distributed fraction of donors and acceptors, and the other from the clustered molecules:

where f_random and f_clustered are the molar fractions of randomly distributed and clustered donors, respectively. E_random is the energy transfer efficiency for the randomly distributed molecules (Eq. A1 or A2), and E_clustered is the energy transfer efficiency of clustered molecules (for example, from Eq. A4 for dimers). It immediately follows from this equation that because E_random is a function of the acceptor surface density (Eqs. A1 and A2), E_mixture would also depend on acceptor surface density. Note that for the sake of simplicity, this model does not include any terms that take into account FRET between clusters or between the clustered and randomly distributed molecules. Such interactions would further depend in more complicated ways on f_clustered, f_random, and the surface density of the molecules of interest.

We will consider two limiting cases for the mixed population described by Eq. A5. The first is the case where regardless of overall surface density of the molecules of interest, the mole fraction of randomly distributed and clustered molecules remains constant, in other words, f_clustered, f_random, and E_clustered are assumed to be constants. Fig. A3,a shows E_mixture calculated for two different values of f_clustered, assuming E_clustered = 37.5% (similar to the example given for Fig. A1,f). The results of this calculation show that, at a single D:A, when 10% of the molecules are clustered, E_mixture is only slightly larger than that predicted for the pure random case, but when 50% of the molecules are clustered, E_mixture is substantially increased over E_random. The magnitude of the difference between E_mixture and E_random will depend on the size of r, since for a given acceptor surface density, E_random becomes smaller as r increases (Fig. A2). However, when clusters are present, E_clustered dominates E_mixture at low acceptor surface densities, where the contribution from the randomly distributed molecules is smallest. Thus, in this case E_mixture will not necessarily extrapolate to zero at low surface densities, while E_random will. Furthermore since E_clustered is a function of D:A (Eqs. A3 and A4), E_mixture will also be sensitive to D:A. This is illustrated in Fig. A3,b, which shows that for a mixture of randomly distributed monomers and dimers, E_mixture increases as a function of increasing mole fraction of acceptor in the D:A mixture (Fig. A3 b).

The second limiting case that we will consider for mixed populations occurs when the fraction of clustered versus randomly distributed molecules depends on the surface density of the molecules of interest. To explore this effect, we will use a well-defined model in which acceptors directly bind to randomly distributed donors (Wolber and Hudson, 1979). Although this model is somewhat different from the others that we have discussed (because it assumes that the donors and acceptors are on two different kinds of molecules that form heterodimers), we present it here because it is a clear example of surface density– dependent clustering. E_mixture for this case can be calculated from Eq. A5 by letting f_random and E_random describe the unbound donors, and f_clustered and E_clustered describe the acceptor-bound donors. The model assumes that one donor-labeled molecule binds to one acceptor-labeled molecule, such that f_clustered = c_A/c_D. Thus f_clustered, f_random, and E_random are all dependent on the donor surface density, the acceptor surface density, or both. Fig. A3,c shows E_mixture calculated for several values of donor surface density c_D, setting E_clustered = 50% for a heterodimer. These model calculations show that the contribution of clusters to E_mixture is small at low surface densities but becomes increasing large with increasing acceptor surface density (Fig. A3,c). This contrasts with the case discussed above (constant f_clustered) where E_mixture is nonzero even in the limit of low surface densities (Fig. A3, a and b). Finally, since c_D and c_A are proportional to D:A, again in this case E_mixture depends on D:A.

The theoretical models presented above predict both quantitative and qualitative differences in E for randomly distributed, clustered, and mixed populations. If parameters such as the value of r and the geometry of presumed clusters are known, the models could be tested quantitatively by directly comparing the theoretical curves and experimental data. However, even the qualitative differences between these various models should be sufficient to distinguish among them. These differences can be revealed experimentally by asking: (a) Is E dependent on either donor or acceptor surface density; (b) does E go to zero at low surface densities; and (c) is E is sensitive to D:A? The predicted results for each of the distributions are summarized in Table I in the Results section.