FRET Spectrometry: A New Tool for the Determination of Protein Quaternary Structure in Living Cells

Abstract

Förster resonance energy transfer (FRET) is an exquisitely sensitive method for detection of molecular interactions and conformational changes in living cells. The recent advent of fluorescence imaging technology with single-molecule (or molecular-complex) sensitivity, together with refinements in the kinetic theory of FRET, provide the necessary tool kits for determining the stoichiometry and relative disposition of the protomers within protein complexes (i.e., quaternary structure) of membrane receptors and transporters in living cells. In contrast to standard average-based methods, this method relies on the analysis of distributions of apparent FRET efficiencies, E_app, across the image pixels of individual cells expressing proteins of interest. The most probable quaternary structure of the complex is identified from the number of peaks in the E_app distribution and their dependence on a single parameter, termed pairwise FRET efficiency. Such peaks collectively create a unique FRET spectrum corresponding to each oligomeric configuration of the protein. Therefore, FRET could quite literally become a spectrometric method—akin to that of mass spectrometry—for sorting protein complexes according to their size and shape.

Introduction

Many cellular processes rely on dynamic interactions between different parts of the same protein (i.e., conformational changes) or between a protein and other proteins of its own (homo-oligomerization) or a different kind (hetero-oligomerization), between proteins and ligands (ligand binding), or between proteins and other macromolecules, such as DNA. Although such interactions are commonly studied in vitro using biochemical methods, it is not easy to translate the information gained in in vitro studies to in vivo situations.

Colocalization of macromolecules using fluorescence microscopy has traditionally been the most popular method to study proteins in living cells. Recent years have seen a dramatic growth in the area of cellular and molecular imaging using fluorescence from spectral variants of the green fluorescent protein (GFP) (1,2), as well as other, non-GFP molecules (3). Since the proteins are a few nanometers wide, whereas the resolution of the fluorescence microscopy is on the order of hundreds of nanometers, localization (or colocalization) of proteins inside the cell does not provide enough information to also identify interactions between the proteins (4).

Microscopy based on Förster resonance energy transfer (FRET)—a process through which energy from an excited donor molecule (D) is transferred nonradiatively to a nearby unexcited acceptor molecule (A) (5–7)—provides the needed information for detection of protein-protein interactions, as it only occurs between fluorophores separated by <10 nm. Let us consider an ensemble of donors and acceptors subjected to excitation by light with a wavelength at which the donors are optimally excited but the acceptors are not. When the donors and acceptors are far apart, i.e., noninteracting, the donors fluoresce brightly. If they move close together, energy may be transferred through coupling between the transition dipoles of the donor and acceptor, causing the donor emission to become dimmer while the acceptor brightens. A different, but related, effect is the decrease in the lifetimes of the interacting donors, since FRET provides the donors with additional pathways for deexcitation, which causes them to lose their excitation sooner.

These three effects—i.e., reduced emission (or quenching) of the donor, enhanced (or sensitized) emission of the acceptor, and shortened lifetime of the donor—form the basis for numerous FRET-based imaging investigations published in the literature. For instance, Parsons and co-workers (8) used FRET to analyze the molecular interactions and conformational changes in various proteins involved in the regulation of cell adhesion and motility. Lleres and co-workers (9) used FRET in conjunction with multiphoton fluorescence lifetime imaging microscopy (FLIM; see below) to study chromatin compaction in living cells at the scale of nucleosomal arrays. Albizu et al. (10) used time-resolved FRET to detect the oligomerization of G-protein-coupled receptors in their native tissues. Chen and co-workers measured the energetics of the GpA transmembrane domain dimerization in vesicles derived from mammalian membrane (11). Stoneman et al. used commercially available Premo Cameleon FRET biosensors (Life Technologies, Carlsbad, CA) to probe induced calcium-ion concentration changes within the cell (12).

Many of these, as well as other, applications of FRET have been discussed extensively in review articles and books (see, e.g., Lakowicz (7), Selvin (13), and Raicu and Popescu (14)). In this minireview, we first present an overview of the theoretical and experimental underpinnings of FRET, which we then build upon, introducing a steadily expanding area of research that is expected to result in the full development of FRET as a spectrometric method for quaternary structure determination in vivo.

Overview of the Principles of FRET-Based Imaging

Donor dequenching via acceptor photobleaching

When an incident photon is absorbed by a fluorescent donor (D), an electron jumps to an excited singlet state, S_1, from the ground state, S₀. The electron quickly loses some of its energy through vibrational relaxation and decays to the lowest vibrational level in S₁. It then decays to the ground state, S₀, either by emitting a red-shifted photon, with rate constant Г^r,D (where the superscript r stands for radiative), or through nonradiative (nr) processes, with rate constant Г^nr,D.

The quantum yield of the excited donor (or the quantum yield of the fluorescence process) is defined as the fraction of excitations lost through photon emission (Г^r,D) relative to the total number of photons absorbed; the latter is proportional to the sum of the numbers of excitations lost through all deexcitation processes available to the donor (Г^r,D + Г^nr,D). Thus (14,15),

$$Q^D=\frac{{\Gamma }^{r,D}}{{\Gamma }^{r,D}+{\Gamma }^{nr,D}}.$$ (1)

If the donor energy can be transferred to an acceptor (A) that presents suitable absorption properties and orientation of its transition dipole, the additional deexcitation pathway (caused by FRET) reduces the quantum yield of the donor fluorescence in the presence of the acceptor according to the following equation (15,16):

$$Q^{DA}=\frac{{\mathrm{Г}}^{r,D}}{{\mathrm{Г}}^{r,D}+{\mathrm{Г}}^{nr,D}+{\mathrm{Г}}^{FRET}}.$$ (2)

The efficiency of the energy transfer, or FRET efficiency, is defined as the fraction of donor excitations that is transferred to the acceptors through FRET, that is,

$$E=\frac{{\mathrm{Г}}^{FRET}}{{\mathrm{Г}}^{r,D}+{\mathrm{Г}}^{nr,D}+{\mathrm{Г}}^{FRET}}.$$ (3)

Combining Eqs. 1–3 leads to the following relation between the quantum yields of the donor in the presence and absence of acceptor:

$$Q^{DA}=Q^D\left(1-E\right),$$ (4)

which suggests that FRET reduces the donor emission by a factor of 1 – E.

To exploit this effect, one first measures the donor emission in the presence of acceptor and then photobleaches the acceptor (by repeated excitation with high-intensity light) to dequench the donor and thus detect its fluorescence in the absence of acceptor (or FRET).

The acceptor-photobleaching method is rather simple and easy to implement. Its main disadvantage is that it is destructive and thus can be used only once for an individual biological sample, which makes it unsuitable for dynamic measurements. It may also be very slow, depending on how long it takes to photobleach the acceptor.

Acceptor sensitized emission

The excitation rate of the acceptors in the presence of FRET increases as described by the equation

$${\mathrm{Г}}^{ex,AD}={\mathrm{Г}}^{ex,A}+{\mathrm{Г}}^{ex,D}E,$$ (5)

where ${\mathrm{Г}}^{ex,AD}$ is the excitation of the acceptors in the presence of donors, and ${\Gamma }^{ex,D}=I_0\left({\lambda }_{ex}\right)/\left(hc{N}_A\right){\epsilon }^D\left({\lambda }_{ex}\right)$ and ${\Gamma }^{ex,A}=I_0\left({\lambda }_{ex}\right)/\left(hc{N}_A\right){\epsilon }^A\left({\lambda }_{ex}\right)$ are the excitation rate constants of D and A, respectively, in the absence of FRET. $I_0\left({\lambda }_{ex}\right)$ is the intensity of the incident radiation, ${\epsilon }^D\left({\lambda }_{ex}\right)$ and ${\epsilon }^A\left({\lambda }_{ex}\right)$ are the extinctions of donor and acceptor at the excitation wavelength ${\lambda }_{ex}$, h is Plank’s constant, c is the speed of the light, and $N_A$ is Avogadro’s number.

The increase in the acceptor excitation rate due to FRET is called acceptor sensitized emission and can be used to detect FRET from measurements of acceptor emission intensity. The sample, which contains both donors and acceptors, is excited at the donor excitation wavelength. In pioneering experiments, the donor and acceptor fluorescence were collected by using filter sets that select for donor and acceptor fluorescence, but spectral-resolution instruments provide better resolution (see below). Due to the small Stokes shift of most fluorescence molecules, the collected acceptor signal is usually contaminated by bleed-through, meaning that the donor emits in the detection channel of the acceptor (and vice versa). Several algorithms have been developed for performing necessary corrections in experiments based on acceptor sensitized emission (17–19). When the interactions between the donors and the acceptors are weak, however, the amount of noise in the final FRET image may exceed the level of sensitized emission because of all the necessary corrections.

Fluorescence lifetime

The fluorescence lifetime of the donor may be defined as the inverse of the rate of deexcitation (15,16), or

$${\tau }_D={\left({\mathrm{Г}}^{r,D}+{\mathrm{Г}}^{nr,D}\right)}^{-1}.$$ (6)

In the presence of acceptors of energy, the lifetime of the donor becomes (15,16)

$${\tau }_{DA}={\left({\mathrm{Г}}^{r,D}+{\mathrm{Г}}^{nr,D}+{\mathrm{Г}}^{FRET}\right)}^{-1}.$$ (7)

Combined with Eq. 3, these two equations yield the expression

$$E=1-\frac{{\tau }_{DA}}{{\tau }_D},$$ (8)

which relates the FRET efficiency to the fluorescence lifetimes of the donor in the presence and absence of acceptor. This provides a convenient means for measuring the FRET efficiency from fluorescence lifetime measurements (7,20,21).

The method based on this effect, called fluorescence lifetime imaging microscopy (FLIM) can be used to determine FRET without being significantly affected by cross-talk artifacts (22–26). Another advantageous feature is that FLIM is not affected by the direct excitation of acceptors, so that even acceptors that are not fluorescent can be used (27). Unfortunately, although technical improvements have increased the temporal resolution of FLIM (28), the acquisition time for the technique is longer compared to the timescale of molecular diffusion. This may alter the molecular makeup of an image pixel during the process of measurement.

Spectral imaging

Recent publications have demonstrated the feasibility of spectrally resolved fluorescence microscopy (29,30) and tested it in quantitative FRET imaging (31–39). In spectral FRET imaging, first the fluorescence intensities are measured at several wavelengths, ${\lambda }_{em}$, for samples containing only A or only D molecules, to obtain emission spectra, i.e., a set of emission intensities at several wavelengths spread uniformly over the emission range (29,30). The fluorescence intensities for every wavelength in these spectra are divided by the maximum intensity value in each spectrum to obtain normalized fluorescence spectra, $s^A$ and $s^D$. Then, the fluorescence intensity of the sample containing both A and D is measured at the same wavelengths and the composite fluorescence spectrum, $S^m$, is recorded. The measured composite spectrum is related to the individual $s^A$ and $s^D$ spectra through the relation

$$S^m=k^{DA}\left({\lambda }_{ex}\right)s^D+k^{AD}\left({\lambda }_{ex}\right)s^A,$$ (9)

where the adjustable parameters $k^{DA}\left({\lambda }_{ex}\right)$ and $k^{AD}\left({\lambda }_{ex}\right)$ are proportional to the fluorescence emission from donors in the presence of acceptors and from acceptors in the presence of donors, respectively. By using a least-squares minimization procedure, it is possible to determine the $k^{DA}\left({\lambda }_{ex}\right)$ and $k^{AD}\left({\lambda }_{ex}\right)$ values (16,36,40) that best fit the measured composite spectrum. By choosing the FRET pairs such that the acceptor molecules are only excited through FRET (i.e., there is no acceptor excitation by light), these quantities may be used to determine the apparent FRET efficiency for each image pixel:

$$E_{app}=\frac{1}{1+\frac{Q^A}{Q^D}\frac{k^{DA}}{k^{AD}}\frac{w^D}{w^A}},$$ (10)

where w^A and w^D are the integrals of the normalized spectra $s^A$ and $s^D$, and Q^A and Q^D are the quantum yields of A and D, respectively. Therefore, $E_{app}$ is determined without recourse to acceptor photobleaching or sequential excitation of the acceptor at two different wavelengths needed to determine donor and acceptor emission baselines. Instead, spectral imaging makes it possible to determine the apparent FRET efficiency with a single sample scan, to avoid complications created by molecular distribution changes associated with molecular diffusion (see below).

This method has been used for the determination of the stoichiometry and geometry of protein complexes in living cells (see below). Its main advantage is that it provides individual E_app values for each image pixel, which allows one to generate distributions of FRET efficiencies, or E_app histograms, by plotting the number of image pixels that fall in a certain interval of E_app values against the center of the E_app interval. Such distributions are obviously richer in information than the average FRET efficiencies of entire cells or cellular regions of interest (41), as will become apparent later. The main disadvantage of this method has been the relatively high cost associated with the experimental system, especially the excitation lasers in the case of two-photon excitation systems, though this issue is actually shared with other techniques, including FLIM. Advances in fiber optics lasers will likely make this technique more affordable in the near future. It is also possible to perform spectrally resolved FRET using single-photon excitation systems (35,36,39,42), such as confocal microscopes.

Theoretical and Experimental Basis of FRET Spectrometry

Overview of the FRET algebra

Although at first sight the mathematics behind the FRET spectrometry might look laborious (15), some simple rules actually can be derived that will allow one to directly record expressions for apparent FRET efficiencies corresponding to different oligomeric configurations without recourse to laborious mathematical derivations.

For an oligomeric complex with a particular configuration (such as the one in Fig. 1) and containing n monomers, of which k are identical donors and n − k are identical acceptors, the average FRET efficiency for all the donors in a given oligomeric configuration can be written as (15)

$$E_{app}=\frac{1}{k}\sum _{i=1}^k{E}_{i,k,n}=\frac{1}{k}\sum _{i=1}^k\frac{\sum _{j=1}^{n-k}{\Gamma }_{i,j}^{FRET}/\left({\Gamma }^{r,D}+{\Gamma }^{nr,D}\right)}{1+\sum _{j=1}^{n-k}{\Gamma }_{i,j}^{FRET}/\left({\Gamma }^{r,D}+{\Gamma }^{nr,D}\right)},$$ (11)

where i and j are summation indices for donors and acceptors, respectively, and ${\Gamma }_{i,j}^{FRET}$ is the rate constant for FRET between single donor-acceptor pairs.

Figure 1.

Illustration of the various ways in which an excited donor can lose its electronic excitations when associated with acceptors. Significance of the symbols: i and j, counting indices for donors and acceptors, respectively; Γ with various superscripts, rate constants of deexcitation; superscript r, a radiative process; superscript nr denotes a nonradiative process other than transfer to the acceptor (such as internal conversion); superscript FRET denotes a Förster resonance energy transfer from D to A.

Based on this equation, one can derive expressions for the apparent FRET efficiency in protein complexes of various sizes (i.e., dimers, trimers, tetramers, etc.) and configurations (e.g., linear versus square-shaped tetramers). In such cases, the apparent FRET efficiency has the meaning of an average efficiency/donor in a complex. For simplicity, we further assume that at most one donor in the complex is in an excited state for any time period and that either static or dynamic averaging of the orientation factor (5) applies. For example, for the tetrameric complex presented in Fig. 1, the apparent efficiency/donor is obtained from Eq. 11 as

$$E_{app}=\frac{3{\Gamma }^{FRET}/\left({\Gamma }^{r,D}+{\Gamma }^{nr,D}\right)}{1+3{\Gamma }^{FRET}/\left({\Gamma }^{r,D}+{\Gamma }^{nr,D}\right)}=\frac{3E_p}{1+2E_p},$$ (12)

where we use the notation $E_p=\left[{\Gamma }_s^{FRET}/\left({\Gamma }^{r,D}+{\Gamma }^{nr,D}\right)\right]/\left[1+{\Gamma }_s^{FRET}/\left({\Gamma }^{r,D}+{\Gamma }^{nr,D}\right)\right]$ for the pairwise FRET efficiency, or the FRET efficiency between a single donor and a single acceptor. Depending on the number of acceptors and donors, as well as their relative positions within the complex, rhombus tetramers could assume several configurations, the configuration shown in Fig. 1 being only one of the possibilities.

The rule that immediately emerges from Eq. 11 (under the approximations made above),

$$E_{app}=\frac{1}{k}\sum _{i=1}^k\frac{n_{A,i}{E}_p}{1+\left(n_{A,i}-1\right)E_p},$$ (13)

where $n_{A,i}$ is the number of acceptors within the range of the ith donor, provides the means to assess those situations. For instance, if the acceptor j = 1 in Fig. 1 is replaced by a donor, the E_app for the new configuration is 1/2 (because of two donors) times the $(2E_p/(1+E_p)+E_p)$. By following this line of reasoning, one can easily obtain expressions for any oligomeric size and configuration; additional useful examples are shown in Fig. 2.

Figure 2.

Apparent FRET efficiency expressions for different sizes and configurations of oligomers. Only FRET-productive configurations (i.e., complexes containing at least one donor and at least one acceptor) are shown. Note that all the efficiencies associated with each type of oligomer depend on a single parameter, the pairwise FRET efficiency, or efficiency of energy transfer between a single donor and a single acceptor (E_p).

The simple rules and sets of equations described above and illustrated in Fig. 2 may be used to extract information regarding the stoichiometry and quaternary structure of protein complexes in living cells by comparing them to the number and relative disposition of the peaks in the E_app histograms determined experimentally.

More precise determinations of the apparent FRET efficiencies for the configurations shown in Fig. 2 (or any arbitrary configuration) are possible, both analytically and using Monte Carlo simulations that take into account all the possible energy-transfer pathways in the complex. For example, it is possible to include transfer along the long diagonal in the rhombus tetramer (43,44), which would lead to small corrections for some of the rhombus configurations. Also, it is possible for nonplanar structure models to give the same (or similar) set of equations as shown in Fig. 2 for planar structures. For instance, one could imagine four-sided structures corresponding to the rhombus tetramer and five-sided structures corresponding to the planar pentamer in Fig. 2. In the interest of simplicity, we will avoid such details in this article.

Selection of the experimental method

Depending on the size (in terms of the number of molecules) of the complex, the proportion of donors and acceptors in the complex, and the geometry of the complex or the relative distances between molecules, E_app histograms may exhibit one or more peaks, whose positions depend on a single parameter, the pairwise FRET efficiency. Such features allow for identification of the quaternary structure of proteins in living cells, as discussed below.

To obtain FRET spectrograms, a fluorescence imaging method must be used that presents molecular resolution and provides FRET efficiency values at each image pixel and therefore meets the following requirements:

• 1.It should allow for complete separation of donor and acceptor signals from measured intensities. This requires temporal, spectral, polarization, or some other kind of resolution of a physical quantity that distinguishes the donor from the acceptor. In this way, donor-acceptor pairs with high spectral overlap can be used that provide high FRET efficiency for increased accuracy of the results.
• 2.It should present molecular-level resolution, so that the signals detected in each image pixel should originate from a single, or just a few, molecular complex(es). That requires both some kind of image-sectioning capability, to reduce the excitation volume, and hence the number of molecules, and high enough sensitivity to detect faint signals from single molecules. Typically, confocal and multiphoton excitation microscopes meet these requirements, whereas wide-field microscopes do not.
• 3.Direct excitation of acceptors by incident light should be negligible, so that acceptors are only excited via FRET. This is needed to avoid unnecessary corrections and, hence, the number of separate measurements necessary to calculate the FRET efficiency for each image pixel. This requirement can be met by choosing fluorescent molecules with large Stokes shifts, so that their emission and excitation spectra are well separated.
• 4.The molecular composition of a region of the sample corresponding to an image pixel should not change during the process of photon collection for that pixel. One common departure from this requirement is when the instrument acquisition speed is so low that the molecular composition of a region of the cell changes over the course of measurements due to molecular diffusion or other kind of dynamics.

The comparative advantages and disadvantages of the fluorescence-intensity-based methods relying on acceptor photobleaching and sensitized emission were discussed briefly in the previous sections. From the standpoint of the FRET spectrometry method presented here, the most important difficulties facing those techniques is that both of them require multiple scans of the sample and do not meet the first and fourth of the requirements listed above.

For intensity-based imaging methods to meet conditions 1 and 4 above, spectral resolution is needed so that the donor and acceptor signals can be determined simultaneously by unmixing of a composite fluorescence spectrum based on knowledge of individual D and A spectra. The spectral resolution has to be achieved in such a manner that signals at each emission wavelength are determined simultaneously (i.e., through parallel acquisition) so that the molecular diffusion does not scramble the spectra. These assumptions were used in the derivation of Eq. 10 above (31–38).

As for the lifetime measurements, although current methods satisfactorily address condition 1 one above, they do not easily meet condition 4. To increase the signal/noise ratio in FLIM measurements, one usually bins together several adjacent pixels in the acquired image. This binning leads to undesired mixing of the signals originating from different pixels and corresponding to different configurations of donors and acceptors within oligomers, each of which gives a different fluorescence lifetime. In addition, the comparatively low acquisition speed of most FLIM techniques leads to mixing of signals from different complexes diffusing through the sample voxel during signal acquisition, which causes them to also violate requirement 2. The resulting large number of lifetimes accumulated in the same pixel (binned or not binned, as is the case) causes important difficulties in fitting the experimental data with exponential decay functions corresponding to several different lifetimes (e.g., at least six for tetramers) (33). It is our hope that this situation will be remedied in the future through development of faster and more sensitive techniques for lifetime measurements.

Analysis of FRET Efficiency Distributions

E_app histograms

In practice, apparent FRET efficiency distributions obtained from the experiments are interpreted based on simulated distributions, such as those corresponding to the different models in Fig. 2. To this end, for a certain quaternary structure model to be tested, a sum of Gaussian peaks is simulated, in which the center of each peak corresponds to an E_app value that in turn corresponds to one of the donor-acceptor configurations. The model that produces the best agreement between the peak positions of simulated and experimental E_app distributions is taken as the quaternary structure of the protein. Since such peaks collectively create a unique FRET spectrum where each peak corresponds to an oligomeric configuration of the protein, it could be called a FRET spectrum or spectrogram—in effect, histograms associated with the distributions of apparent FRET efficiencies. In this manner, FRET becomes a spectrometric method, akin to that of mass spectrometry, for sorting out protein complexes according to their size and shape. We want to emphasize here that the fluorescence spectra used to separate donor from acceptor signals in the spectral-imaging method should not be confused with the concept of E_app spectra introduced in this article.

The FRET spectrometry method performs best if the protein complexes are stable structures and their expression level is so low that one voxel in the sample space contains a single protein complex. If this approximation is not valid in practice, one needs to take into consideration the averaging effects introduced by colocalization (in the same sample voxel) of protein complexes of different configurations and sizes.

Recently, measurements employing a two-photon microscope with spectral resolution and FRET (33) were used to determine the number (i.e., the association stoichiometry) and relative disposition (i.e., structure) of protomers within homo-oligomers of a model G-protein-coupled receptor (45), the sterile-2 α factor receptor (Ste2p) in the yeast Saccharomyces cerevisiae. Yeast cells were engineered to express the fusion proteins Ste2p-GFP₂ and Ste2p-yellow fluorescent protein (YFP) in their plasma membrane without interference from endogenous (33). Fig. 3 presents typical results obtained for a cell coexpressing Ste2p-GFP₂ and Ste2p-YFP in its plasma membrane and compares them with results obtained from an artificial dimer expressed in the cytoplasm of the same cell type. Using separately measured emission spectra of the two tags and a spectral decomposition method (36), we unmixed the composite fluorescence spectra obtained at each image pixel from cells expressing Ste2p-GFP₂ and Ste2p-YFP to obtain donor (Fig. 3 a) and acceptor signals (Fig. 3 b), respectively. From these images, the apparent FRET efficiency (E_app) was estimated for each image pixel (Fig. 3 c). FRET efficiency histograms were generated (Fig. 3 d) by binning together the pixels with similar FRET efficiencies, which presented multiple peaks for Ste2p and a single major peak for the obligate dimer GFP₂-YFP. Of the several models used to simulate the experimental distribution of E_app from Ste2p, a model of a tetramer configured as a rhombus (see Fig. 2 above) provided the best fit, although mixtures with smaller oligomers were not ruled out in this study.

Figure 3.

Results obtained from spectral FRET from cells expressing the fusion proteins Ste2p-GFP₂ and Ste2p-YFP in internal and plasma membranes of yeast (S. cerevisiae) (upper row) and GFP₂-GG-YFP in the yeast cytoplasm (lower row). (a and b) Spectral images obtained from measurements with a two-photon microscope with spectral resolution were unmixed (36) to obtain the donor (k^DA) and acceptor (k^AD) signals for each pixel. (c) From the signals obtained, the pixel-level apparent FRET efficiency (E_app) was calculated according to Eq. 10. (d) The FRET efficiency map shown in c was used to generate the distribution of measured FRET efficiencies. Data points represent the experimental distributions. The data were fitted to a sum of five (upper row) or two (lower row) Gaussians shown individually (thin green lines) or as a sum (thick red line).

In an attempt to better control the ratio between the concentrations of donors and acceptors expressed by the cells, Patowary et al. (32) used cells engineered to express a form of the muscarinic M₃ acetylcholine receptor (M₃R) tagged with an energy acceptor to remain at a constant amount, while levels of an energy-donor-tagged form of this receptor could be titrated from an inducible locus (46). Specifically, they investigated the quaternary organization and degree of stability of M₃R at the plasma membrane. The largest oligomeric structure present was identified from the number and relative disposition of peaks within an E_app histogram, which, as for Ste2p, turned out to be a rhombus tetramer. This model was confirmed by observing an increase in the amplitudes of the first peaks in the histogram (corresponding to the configurations shown in Fig. 2) and decrease in the amplitude of the peaks on the righthand side of the histogram as the donor concentration was increased by almost an order of magnitude. Further data analysis of the complexes located at the plasma membrane indicated that there was an excess in the amplitude of the second histogram peak (centered at E_p) compared to what was predicted by a simple binomial distribution of amplitudes for a tetramer. This amplitude excess was interpreted as originating from the presence of dimers in addition to tetramers. Thus, at the plasma membrane, homomers of the M₃R exist as a mixture of dimers and rhombic tetramers.

E_app metahistograms

From these two examples, it appears clearly that pixel-level FRET provides invaluable biological information regarding stable (i.e., long-lived) oligomeric complexes in living cells. However, when either the expression level is very low or the proteins rapidly associate and dissociate to produce uniform distributions of complexes with the same proportion of donors and acceptors throughout the cell, it becomes difficult to apply the E_app histogram method without a priori knowledge of E_p. This is because, in such cases, the FRET efficiency histograms present a few or even single peaks, which may easily leave one with the incorrect impression that the protein in question forms dimers, whereas in fact it may form higher-order oligomers. In a recent study (31) of the oligomerization of Wzm and Wzt subunits of a bacterial ABC transporter, a method was introduced according to which the positions of single (or dominant) peaks in such histograms were collected and binned to form so-called metahistograms of peak positions. An unintended, though fortunate, consequence of the metahistogram approach is a dramatic reduction of the degree of blur between the peaks, which aids significantly in the determination of the appropriate structural model. In the particular study mentioned above, the metahistograms agreed well with the predictions of a square homo-tetramer model for both the Wzm and Wzt subunits.

The price to pay for all the convenient features of the metahistograms is that nondominant peaks in the original (i.e., cell-level) histograms are ignored, and therefore, the method cannot be used to determine frequencies of occurrence of the different donor-acceptor configurations from the amplitudes of the peaks. This makes it harder to resolve the different oligomeric species from mixtures of oligomers of different sizes and/or geometries, especially for high expression levels of protein. The metahistogram method is therefore most useful as a first step in trying to identify the oligomeric structure that produces the largest number of peaks in the experimental E_app distribution for low expression level of protein.

Such limitations notwithstanding, preliminary computer simulations for distributions of oligomeric complexes across image pixels indicate that for mixtures of dimers and monomers, the histogram approach should remain useful even for arbitrarily high concentrations of molecules, as long as the concentration of the free donors does not overwhelm that of the dimers (41). Briefly, the explanation for this is as follows. Concentrations of molecules per pixel corresponding to much less than one donor-acceptor pair (i.e., a dimer) or one monomeric donor generate single peaks in the histogram, which will always appear at the same position along the horizontal axis (within experimental error); consequently, the metahistogram of such peak positions will also present a single peak. For higher expression levels, D-A and D-D dimers, as well as free donors, mix at pixel level, thereby generating additional peaks in the metahistograms depending on the total number of donors present (Eq. 11). Since expression level naturally varies from cell to cell, additional peaks in the histograms will appear to the left of the dimer’s FRET efficiency for each combination of D-A and D-D complexes and monomeric dimers per pixel. Such peaks therefore could be regarded as a fingerprint of the dimer at high concentrations. If additional peaks are obtained, or the histogram is severely smeared for high expression levels, higher-order oligomers must be forming.

Before concluding this section, a word of caution is necessary. The metahistogram approach can provide misleading information when the following two conditions exist simultaneously: 1) proteins associate into oligomeric complexes larger than dimers (i.e., trimers, tetramers, etc.), and 2) the average concentration of such oligomers is greater than one complex/sample voxel.

Conclusions

Although we have shown that the studies performed to date relying on FRET spectrometry (as described above) provided very useful results regarding protein assembly into oligomers, this area of research is still rapidly developing. Detailed investigations have yet to be performed on numerous other proteins to determine their number of subunit protomers and quaternary structures. In doing so, particular attention needs to be devoted to producing reliable tests for distinguishing between, for example, tetrameric structures and combinations of oligomers of different sizes or even combinations of dimers and monomeric donors. All of these situations could be characterized by broad E_app distributions with numerous peaks or more complicated features, the relative dispositions of which need to be carefully evaluated using statistical tests.

An intriguing possibility is to combine the quaternary structure information obtained from FRET spectrometry studies with results of molecular dynamics simulations (47) of such quaternary structure models to determine binding interfaces between protomers within a complex and to aid in the understanding of the oligomer function. To this end, one can start by positioning and orienting the protomers (with known tertiary structure) within an oligomer such that the fluorophores of the fluorescent tags roughly obey the distance constraints obtained from FRET spectrometry. Because the relative orientation of the fluorescent tags is not known, this first step implicitly assumes the orientational average over a cylinder, which would be valid for membrane proteins to which the tags are attached by linkers that permit a high degree of rotational freedom for the tags. If, by contrast, rotational diffusion of the tags is impeded by steric or other constraints, a second step should be added in which coarse-grained molecular dynamics simulations of the rotational diffusion of the fluorescent tags and their known linkers are used to determine the most probable orientation of the transition dipoles of the fluorescent tags. In this way, the orientation factor in FRET, or the κ² of the molecules (see, e.g., pertinent studies in the literature (5–7,48) for a definition of κ² and its effect on FRET efficiency), can be computed, and these values can then be used in a third step to obtain a more accurate value of the pairwise FRET efficiency using Monte Carlo simulations of FRET in the complex (44,47,48) and to determine new interprotomer distances from FRET spectrograms. Next, the new distance values can be used to adjust the position and orientation of the protomers, and the whole process can be repeated iteratively until the molecular dynamics simulations converge toward an oligomeric structure with the lowest potential energy that also obeys the distance constraints from FRET.

Although this approach will undoubtedly present investigators with its own set of challenges, it appears to be feasible with the use of existing powerful computers. We suggest that the end result—identification of the binding interfaces between protomers within a complex—warrants the effort, as it will facilitate an understanding of the functional role of such complexes in living cells.