Oligomerization of the tetramerization domainof p53 probed by two- and three-colorsingle-molecule FRETHoi Sung Chunga,1, Fanjie Menga, Jae-Yeol Kima, Kevin McHalea, Irina V. Gopicha, and John M. Louisa

aLaboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520

Edited by Taekjip Ha, Johns Hopkins University, Baltimore, MD, and approved June 29, 2017 (received for review January 7, 2017)

We describe a method that combines two- and three-color single-molecule FRET spectroscopy with 2D FRET efficiency–lifetime analy-sis to probe the oligomerization process of intrinsically disorderedproteins. This method is applied to the oligomerization of thetetramerization domain (TD) of the tumor suppressor protein p53.TD exists as a monomer at subnanomolar concentrations and formsa dimer and a tetramer at higher concentrations. Because the disso-ciation constants of the dimer and tetramer are very close, as wedetermine in this paper, it is not possible to characterize differentoligomeric species by ensemble methods, especially the dimer thatcannot be readily separated. However, by using single-moleculeFRET spectroscopy that includes measurements of fluorescence life-time and two- and three-color FRET efficiencies with corrections forsubmillisecond acceptor blinking, we show that it is possible toobtain structural information for individual oligomers at equilibriumand to determine the dimerization kinetics. From these analyses, weshow that the monomer is intrinsically disordered and that the di-mer conformation is very similar to that of the tetramer but the Cterminus of the dimer is more flexible.

single-molecule spectroscopy | three-color FRET | intrinsically disorderedprotein | p53 oligomerization | fluorescence lifetime

It is well known that intrinsically disordered proteins (IDPs) canfold into different structures when attaching to their binding

targets. This structural flexibility and binding promiscuity arerequired for the formation of protein–protein interaction net-works in various biological processes such as signal transductionand gene transcription (1–3). On the other hand, some IDPs self-assemble and form oligomers, many of which are implicated inthe development of diseases such as Alzheimer’s disease (amy-loid-β protein) (4, 5) and Parkinson’s disease (α-synuclein) (6).An ensemble of these oligomers with different sizes and confor-mations is not easy to separate, and therefore, their character-ization is very difficult. However, single-molecule spectroscopy canbe a very powerful tool because it can probe subpopulations in amixture without the need for separation. Single-molecule spec-troscopy has been successfully used for characterizing individualmolecular states such as the folded and unfolded states of proteins(7–9), intermediate states (10, 11), and transition paths (12–17)and for identifying specific molecular species and complexes(18–22). In this paper, we describe the development of a single-molecule fluorescence method that probes individual oligomersin a mixture, characterizes their conformations, and determinesoligomerization kinetics.We have used two- and three-color Förster resonance energy

transfer (FRET) spectroscopy. Compared with two-color FRETthat monitors a single distance, three-color FRET can determinethree distances and therefore has great potential to obtain 3Dstructural information for a molecule or a molecular complex.Multicolor FRET has been demonstrated for well-known anddesigned molecular systems (23–27) and used for the molecularidentification (24, 28, 29) and investigations of conformationalchanges and dynamics of proteins and nucleic acids (30–35) andtheir interactions (36–38). In some cases, the experiment and

analysis can be simplified by preventing the energy transfer be-tween one dye pair (e.g., much larger separation than the Försterradius). However, multicolor FRET experiments are generallycomplex due to technical difficulties in site-specific labeling andpoor photophysical properties of an additional fluorophore. Thiscomplication makes the accurate determination of FRET effi-ciencies challenging, and only a few studies have determined andused all FRET efficiency values (24–26, 36, 37). In this paper, wepresent various analysis methods to overcome these problemsand determine FRET efficiencies accurately. In addition to theFRET efficiency, we also use fluorescence lifetimes to analyzethe correlation between the FRET efficiency and the fluores-cence lifetime in the two-color experiment. From the 2D FRETefficiency–lifetime analysis (39–44), it is possible to not only dis-tinguish conformational states but also estimate the conformationalflexibility of each state. For this analysis, accurate determination ofthe FRET efficiency and lifetime is very important. In addition totypical correction procedures for background, donor leak into theacceptor channel, and detection efficiencies and quantum yields ofdyes (γ-factor), we present a correction method for fast acceptorblinking, which causes a 5–10% error in the determination of theFRET efficiency and donor lifetime. The acceptor blinking effectcan be easily missed because it is faster than the bin time of 10–20 ms and does not clearly appear in FRET efficiency trajectories.In this work we have applied this development in single-

molecule FRET spectroscopy to the oligomerization of the tet-ramerization domain (TD) of the tumor suppressor proteinp53. Atomic-resolution structures are available for the tetramer(45–47), but due to the very small dissociation constant, it is notpossible to characterize the monomer and dimer conformations

Significance

Intrinsically disordered proteins often form pathological oligo-mers implicated in various diseases. In many cases, these oligo-mers cannot be separated and characterizations of their sizesand conformations are difficult. We develop a single-moleculefluorescence method that can probe individual oligomerswithout separation and determine the equilibrium constantsand oligomerization kinetics. By combining two- and three-colorsingle-molecule FRET spectroscopy with fluorescence lifetimeanalysis, it is possible to determine conformations and flexibilityof individual oligomers unambiguously. We apply this methodto the oligomerization of the tetramerization domain of p53 andcompare conformations of monomer, dimer, and tetramer. Thismethod will be useful in exploring other protein oligomerizationsystems involved in important biological and disease processes.

Author contributions: H.S.C. designed research; H.S.C. performed research; F.M., J.-Y.K.,K.M., and J.M.L. contributed new reagents/analytic tools; H.S.C. analyzed data; H.S.C.,I.V.G., and J.M.L. wrote the paper; and H.S.C. and I.V.G. developed theory and analysis.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: chunghoi@niddk.nih.gov.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1700357114/-/DCSupplemental.

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using ensemble measurements. [The solution NMR structurehas been obtained for a destabilized mutant dimer that does notform a tetramer (48).] Although the dimerization and the tetra-merization occur sequentially as the concentration is increased(49), the two dissociation constants are very similar for the TDconstruct used in this work (residues 319–360 of the full-lengthp53), which makes the dimer characterization difficult even bysingle-molecule methods. We show that the dissociation constantsof the dimer and the tetramer and the dimerization kinetics can,however, be determined in single-molecule free-diffusion experi-ments. By immobilizing molecules, we could selectively detectdimers and determine the FRET efficiency and fluorescencelifetime more accurately from longer trajectories. Combination ofthe two- and three-color FRET experiments and the 2D FRETefficiency–lifetime analysis shows that the monomer is disorderedand the dimer conformation is very similar to that of the tetramerbut the C terminus of the chain is more flexible.

ResultsTwo- and Three-Color FRET Experiments and Fluorescence LifetimeAnalysis. In the two- and three-color FRET experiments, wemeasured both fluorescence intensities and lifetimes by usingpicosecond-pulsed laser excitation (Fig. 1A) and a confocal mi-croscope. Compared with three-color FRET, two-color FRETexperiments and the data analysis are relatively simple andstraightforward because energy transfer occurs between only onepair of fluorophores. On the other hand, in the three-color ex-periment, there are three energy transfer efficiencies, whichcannot be determined by a single laser excitation. The excitationof the donor (D) leads to the energy transfers to both acceptors(FRET efficiencies E1 and E2). In addition, the transferred en-ergy to acceptor 1 (A1) can be further transferred to the secondacceptor (A2) (Fig. 1B). To determine all three FRET effi-ciencies, an additional excitation of A1 is required. In this exci-tation, there is only a single energy transfer from A1 to A2. Afterdetermining this FRET efficiency (E12), it is possible to obtain E1and E2 as well (SI Materials, Methods, and Theory, FRET Effi-ciency Calculation and Standard Corrections in Two- and Three-Color Experiments). We used the alternating laser excitationscheme (24, 50, 51) with two picosecond-pulsed lasers (485 nmand 640 nm) for the excitation of Alexa Fluor 488 (Alexa 488, D)and Alexa Fluor 647 (Alexa 647, A1) with the alternating fre-quency of 40 MHz.The pulsed excitation of fluorophores allows for recording

delay times between the laser excitation pulse and the photonarrival in addition to the absolute photon arrival times (Fig. 1A).The absolute arrival times are used to construct fluorescencetrajectories. The mean delay times determine fluorescence life-times (SI Materials, Methods, and Theory, Instrument ResponseFunction and Determination and Correction of FluorescenceLifetimes and Fig. S1). The mean FRET efficiency and donor (oracceptor) lifetime values are used to construct 2D FRETefficiency–lifetime distributions.In the two-color immobilization experiment, a TD monomer

labeled with a donor dye (Alexa 488, D) at its C terminus (TD-D)was immobilized on a glass surface and incubated with 10 nM TDlabeled with an acceptor dye (Alexa 647, A1) at either the N(A1-TD) or the C terminus (TD-A1) (Fig. 2B). Molecules wereexcited by a 485-nm laser in the pulsed mode at 20 MHz. Todetermine the dimerization kinetics, free-diffusion experimentswere carried out to collect fluorescence bursts after manuallymixing 40 pM of TD-D with A1-TD or TD-A1 at various con-centrations. In the three-color immobilization experiment, thedonor- and acceptor-labeled TD monomer (D-TD-A1) wasimmobilized and incubated with 10 nM TD labeled with acceptor2 (Alexa 750, A2) at the C terminus (TD-A2).For the accurate determination of the FRET efficiencies and

lifetimes, we performed various corrections (52). The detailedcorrection procedures of the FRET efficiency and lifetime aredescribed in SI Materials, Methods, and Theory, FRET EfficiencyCalculation and Standard Corrections in Two- and Three-Color

Experiments. The corrections for the background photons anddonor leak are straightforward. We found that the difference ofthe detection efficiencies and quantum yields (γ-factor) and di-rect excitation of the acceptor by a donor excitation laser can becorrected together. In addition, although fast photoblinking onthe timescale of milliseconds and shorter was not visually de-tectable in the trajectories with the bin time of 20 ms (Fig. 3A),the correlation analysis of photon trajectories clearly showsblinking of fluorophores (Fig. S2A). No correction was neededfor donor blinking because it does not change FRET efficienciesand lifetimes. However, during acceptor blinking, only donorphotons are detected and this decreases the mean FRET effi-ciency. In addition, the fluorescence lifetime of these photons islonger than that in the presence of the active acceptor, whichincreases the donor lifetime. The effect of acceptor blinking islarger in the three-color experiment, in which A1 is excited moreby alternating excitation. For each individual trajectory, we madecorrections for acceptor blinking, using the population of theacceptor in the bright state. The acceptor bright-state populationwas determined using the maximum-likelihood method, analyzingphoton trajectories directly without binning (53–55). The detailedcorrection procedures of the FRET efficiency and lifetime aredescribed in SI Materials, Methods, and Theory, FRET Efficiencyand Lifetime Corrections for Acceptor Blinking. We also discuss thecomplex photophysics of Alexa 488 and Alexa 647 (SI Materials,Methods, and Theory, Photophysics of Alexa 488 and Alexa 647)that should be carefully scrutinized before the analysis.

C

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D*A A1 2 DA1 2*A

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ET2

D D0(= 1/ ) A1 A1

0(= 1/ ) A2 A20(= 1/ )

485 nm

640 nmDA1A2

Fig. 1. Three-color FRET. (A) A schematic representation of a photon se-quence of three fluorophores detected after alternating laser excitation(40 MHz). For each photon, the absolute arrival time (t) and the delay time δtbetween the laser pulse and the photon arrival are recorded. All three typesof photons [donor (D), green circles; acceptor 1 (A1), red circles; acceptor2 (A2), purple circles] are detected by excitation of the donor (485 nm, bluedashed lines) whereas only A1 and A2 photons are detected by excitation ofA1 (640 nm, red dashed lines). Photons from the two excitations (i and j areindexes of photons from D and A1 excitation) can be separated (second andthird rows) using their delay times. (Fluorescence lifetimes are much shorterthan the interval between alternating laser pulses, 25 ns.) (B) FRET effi-ciencies between dye pairs. E1 and E2 are the energy transfer efficienciesfrom D to A1 and A2, respectively, and E12 is the FRET efficiency from A1 toA2. (C) Kinetic scheme for three-color FRET. After excitation of the donor(DA1A2 → D*A1A2), the donor decays to the ground state radiatively (rippledarrow) or nonradiatively (dashed arrow), or the energy is transferred to ei-ther A1 (DA1*A2) or A2 (DA1A2*), with the energy transfer rates of kET1 andkET2. Excited A1 decays to the ground state or the energy is further trans-ferred to A2 with the rate of kET12. A1 excitation results in the energytransfer only from A1 to A2. kD, kA1, and kA2 are the sums of the radiativeand nonradiative relaxation rates of the three dyes, which are equal to theinverse of the excited-state lifetimes in the absence of the energy transfer,τD0, τA10, and τA20, respectively.

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Characterization of TD Oligomerization by Two-Color FRET Experiment.We first investigated the oligomerization of TD using two-colorFRET, which is simpler to interpret. Because the atomic resolu-tion structure of the tetramer conformation is known (Fig. 2A)(46), our main focus was to obtain the dimer conformation inisolation at a low concentration. For this purpose, we performedexperiments with two binding constructs shown in Fig. 2B. A TDmonomer labeled with a donor dye (Alexa 488, D) at its C ter-minus (TD-D) was immobilized on a glass surface and incubatedwith 10 nM TD labeled with an acceptor dye (Alexa 647, A1) ateither the N (A1-TD) or the C terminus (TD-A1), so that wecould obtain distance information between the N and C terminiand between the C termini of the two monomer chains in thedimer state (Fig. 3 and Fig. S3).Representative donor and acceptor fluorescence trajectories

are shown in Fig. 3A. A majority of the trajectories exhibited aconstant FRET efficiency without any transition, followed byeither donor or acceptor photobleaching (Fig. S4A). This resultindicates that the dimerization kinetics are much slower than thetens-of-seconds duration of the trajectories. Therefore, theFRET efficiency and donor lifetime distributions in Fig. 3B wereconstructed from the mean values of the FRET efficiency anddonor delay time of the first segment (before photobleaching) ofeach trajectory (i.e., each molecule). There are three peaks bothin the FRET efficiency distributions and in the donor lifetimedistributions. The peak colored in green at E = 0 corresponds tothe monomer and a small fraction of the oligomers with only anactive donor dye (due to incomplete acceptor labeling or inactiveacceptor), whereas the orange peaks (E > 0) correspond tooligomers containing both active donor and acceptor dyes. Thepeaks at E ∼ 0.5 of A1-TD and E ∼ 0.45 of TD-A1 (Fig. 3B,Upper) are expected to correspond to the dimer, assuming thatthe structure of the isolated dimer is similar to that in the tet-ramer (48). (The distance between the C-terminal residues of thelabeled chains 1 and 2 is comparable to the Förster radius R0 =5.2 nm; Fig. 2A.) In addition to these peaks, there are un-expected peaks at E ∼ 0.7 (A1-TD) and E ∼ 0.8 (TD-A1). In-terestingly, these high FRET efficiency peaks disappear after theaddition of a large excess of unlabeled TD (Fig. 3B, Lower),which leads to the formation of the tetramer consisting of a dimerwith a donor-labeled monomer and an acceptor-labeled monomer(chains 1 and 2) and an unlabeled dimer (chains 3 and 4). Thehigh-E peak is not an artifact caused by immobilization of the

proteins because similar distributions are observed in the freediffusion experiment (see Dimerization Kinetics Measured by FreeDiffusion Experiment). Anisotropy measurement also rules out thepossibility of fluorophore sticking (Fig. S5).The presence of the two peaks at E = 0.45–0.5 and E = 0.7–

0.8 may suggest that two stable conformations exist in the dimerstate. However, it turns out that the high-E peak is not a seconddimer state, but corresponds to the tetramer. To show this, weconstructed a transition map from the trajectories exhibiting tran-sitions between high and low FRET efficiencies. If there were twodimer states, these transitions would be reversible because there isonly one tetramer conformation (46). However, the transitions arealmost unidirectional toward the low-E state (Fig. 4A and Fig. S4B).In addition, multiple transitions are also observed (Fig. S4A, LowerRight trajectory). Therefore, it is more likely that these transitionsresult from an irreversible photobleaching of multiple acceptors inthe tetramer. The acceptor labeling efficiency is not 100%, so thenumber of photobleaching steps in the tetramer varies from one tothree, which is consistent with the trajectories shown in Fig. S4A. Inthe case of C-terminal–labeled TD (TD-A1), the FRET efficiencyhistogram is more widely distributed, and it is possible to assign thedimers and tetramers with combinations of the active and inactiveacceptors (Fig. 4A). The peak at E = 0.8 results from the tetramersthat have an active acceptor in chain 3 and the peak at E ∼ 0.4consists of both the dimer and the tetramers without an activeacceptor in chain 3. The transition map of the E distributionsof A1-TD can be explained similarly (Fig. S4B). In the followingsection, we show that the dissociation constant of the tetramer isvery low and the tetramer is formed even at 10 nM.Because the NMR structure is known for the tetramer, our

goal was to characterize the dimer at a low concentration wherethe tetramer is not formed. However, the coexistence of the di-mer and tetramer due to the similar dimer and tetramer disso-ciation constants makes this difficult. Our problem, then, is toobtain dimer information in the presence of the tetramer. Be-cause the dimer contains only one donor and one acceptor, weselectively analyzed trajectories that exhibit a single acceptorphotobleaching followed by a donor photobleaching (Fig. 3A),which would be dimer trajectories in most cases. Although thesetrajectories are only a small fraction of the entire data (compareFigs. 3B and 4B), it is clear that there is a significant reduction ofthe high-E population (E ∼ 0.7 for A1-TD and E ∼ 0.8 for

A B C

D

Fig. 2. Immobilization of dye-labeled proteins intwo- and three-color FRET binding experiments.(A) Front (Upper) and top (Lower) views of the solutionstructure of the tetramer (PDB ID: 1SAE) (46). Fourmonomer chains are indicated by numbers from 1 to 4.Dimers are formed by chains 1 and 2 and by chains3 and 4. The tetramer is a dimer of these two dimers.Quoted numbers are the average Cα distances be-tween C-terminal glycine residues of 77 NMR struc-tures (46). Note that there would be small differencesbetween these values and the true average distancesof the entire ensemble. (B) In the two-color bindingexperiments, Alexa 488 (D) is attached to theC-terminal cysteine residue of the TD, whichcontains biotin and an unlabeled unnatural aminoacid. This molecule (blue) is immobilized on a poly-ethylene glycol (PEG)-coated glass surface via a biotin–streptavidin linkage and incubated with TD (orange)labeled with Alexa 647 (A1) at the N (A1-TD) or Cterminus (TD-A1). (C) In the three-color binding ex-periment, biotin-attached TD (blue) is labeled withAlexa 488 and Alexa 647 at the N and C termini,respectively, and immobilized. This molecule is in-cubated with Alexa 750 (A2)-labeled TD (TD-A2).(D) Amino acid sequences of three TD constructs.In UA-TD-Cys, a biotin molecule is attached to the lysine residue (blue) in the biotin-accepting sequence (AviTag), and an unnatural amino acid (greenU, 4-acetylphenylalanine) and cysteine (red C) are incorporated between the spacer and the TD sequence and at the C terminus, respectively, for site-specific dye labeling. In Cys-TD and TD-Cys, dyes (A1 or A2) are attached to the cysteine residues.

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TD-A1), suggesting the majority of the data result from the di-mers. (The remaining high-E population corresponds to thetetramer with only one active acceptor.) The low FRET effi-ciency of the dimer suggests that the dimer conformation issimilar to that in the tetramer state.A remaining question is why only the high-E tetramer peak

disappears when an excess of the unlabeled TD is added (Fig.3B). The simplest explanation is that the dissociation/associationkinetics between the tetramer and the dimer are much fasterthan those between the dimer and monomer (49); once a dye-labeled dimer dissociates from a tetramer, it quickly binds anunlabeled dimer, which is in large excess, to form a new tetramerbefore it dissociates into monomers. (All acceptor-labeled TDswill be eventually replaced with unlabeled TD after a long time.)In this case, only one pair of the donor and acceptor locations ispossible in the tetramer (i.e., chains 1 and 2 are labeled with a donorand an acceptor, respectively, and chains 3 and 4 are unlabeled;Fig. 2A). We also note that the mean FRET efficiency of thistetramer (Fig. 3B, Lower) is lower than that of the dimers in Fig.4B both for A1-TD and TD-A1, reflecting a small conforma-tional difference between the dimer and tetramer (Table S1shows the comparison of the FRET efficiencies and corre-sponding distances). The FRET efficiency difference is slightlylarger for TD-A1, suggesting that the conformation of the Cterminus of the helix may be more disordered and flexible in the

dimer state compared with that in the tetramer state, consistentwith the NMR structural data of the mutant dimer (48) and themolecular dynamics simulation result (56) (see Discussion formore explanation).This interpretation on the more flexible C terminus of the

dimer is supported by the estimation of the conformationalflexibility by 2D FRET efficiency–lifetime distributions in Figs.3C and 4C. For a state with a single conformation, where thedistance between the two dyes is fixed, the mean FRET effi-ciency and the lifetime are related as (57)

τD�τ0D = 1−E, [1]

where τD and τD0 are donor lifetimes in the presence and ab-

sence of the acceptor. On the other hand, when there is a distri-bution of conformations that interconvert so rapidly that it doesnot appear in binned trajectories as those in Fig. 3A, the lifetimebecomes longer and the peak shifts above the diagonal in the 2Dplot (39–44). In this case, the donor lifetime is related to themean FRET efficiency E as (43)

τD�τ0D = 1−E+

σc2

1−E, [2]

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Fig. 3. Dimerization and tetramerization of TD probed by two-color FRET. Donor-labeled TD (TD-D) was immobilized and incubated with 10 nM acceptor-labeled TD (A1-TD, A–C, Left, columns 1 and 2; TD-A1, A–C, Right, columns 3 and 4). (A) Representative fluorescence trajectories (20-ms bin time) in the donorand acceptor channels. (B) FRET efficiency histograms (Left) and donor lifetime histograms (Right) were constructed from the mean FRET efficiency and meandonor delay time values obtained from the initial segment of the trajectory of each molecule. Segments containing more than 3,000 photons were included inthe analysis. The FRET efficiency was corrected for background, donor leak into the acceptor channel, γ-factor, and acceptor blinking. The donor lifetime wascorrected for background and acceptor blinking. The donor-only peak at E = 0 (green bars) has contributions from the monomers and a small fraction of theoligomers with inactive acceptors. The dimer and tetramer (with active acceptors) distributions appear at higher FRET efficiency and shorter donor lifetime(orange bars). B, Upper and Lower shows the distribution obtained before and after the addition of a large excess (2.5 μM) of unlabeled TD, respectively.(C) Two-dimensional FRET efficiency–donor lifetime plot. The distribution of the donor-only molecules is centered at E = 0 and the relative donor lifetime(τD/τD0) of 1 (green dots). The distributions of the molecules with both the donor and acceptor dyes are shifted upward from the diagonal line, suggesting thepresence of conformations that interconvert rapidly (main text). The data inside the green rectangles were used to calculate the average FRET efficiency andlifetime values for the estimation of the variance of the FRET efficiency due to these conformational distributions (Eq. 2). Two-dimensional plots using thedonor delay times obtained from acceptor photons and comparison with the results without acceptor blinking correction are presented in SI Materials,Methods, and Theory (Fig. S3).

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where σc2 is the variance of the FRET efficiency distribution of

the underlying rapidly interconverting conformational substates.(Note that this is not the variance of the FRET efficiency peak inthe histograms plotted in Figs. 3 and 4.) For the normalized donor–acceptor distance distribution P(r), the mean FRET efficiency isE=

R∞0 EðrÞPðrÞdr and the variance is σc2 =

R∞0 EðrÞ2PðrÞdr−E2,

where E(r) = 1/[1 + (r/R0)6] is the FRET efficiency when the

donor–acceptor distance is r and R0 is the Förster radius. Theupward shift in the 2D plot indicates the conformational flexibilityof a state. σc

2 ranges between 0 (fixed distance) and 0.25 (a systemwith two equally populated interconverting states with the FRETefficiency values of 0 and 1). For the Gaussian chain model (58)with the root mean-square end-to-end distance equal to the Försterradius, σc

2 = 0.11. For this analysis, it is important to determine the

FRET efficiency and lifetime accurately, which requires the correc-tions mentioned above, including acceptor blinking. (See SI Mate-rials, Methods, and Theory, FRET Efficiency and Lifetime Correctionsfor Acceptor Blinking for the details of the correction procedure.)σc

2 can also be determined from the mean acceptor delay times(Eq. S26), which are not affected by acceptor blinking (44). Thevariance of the FRET efficiency distribution σc

2 in the dimer state(Fig. 4C) is larger than that of the tetramer state (Fig. 3C afterthe addition of unlabeled TD), especially in the experiment withC-terminal labeled TD (TD-A1). This result indicates that theC-terminal region of the isolated dimer is more disorderedas mentioned above (Discussion and Table S1).

Dimerization Kinetics Measured by Free Diffusion Experiment. In theimmobilization experiment above, binding and dissociation arenot detectable because the dimerization kinetics are very slow.Fersht and coworkers showed that the dimer dissociates on thetimescale of tens of minutes, using fluorescence correlationspectroscopy (FCS) (49). Therefore, we performed free diffusionexperiments after mixing solutions manually to determine thedimerization kinetics and the dissociation constants of the dimerand tetramer. Donor (Alexa 488)-labeled TD (TD-D) was in-cubated at a low concentration (40 pM) before the experiment toensure the dissociation of molecules into monomers. Then theacceptor (Alexa 647)-labeled TD in a stock solution (100 nM,measured by absorbance of Alexa 647) was diluted into the do-nor solution (Fig. 5A). After dilution, acceptor-labeled TD dis-sociates and then associates with the donor-labeled monomer.The time-dependent FRET efficiency histograms are shown in

Fig. 5B. They consist of a donor-only peak and a distributioncorresponding to the donor- and acceptor-labeled species (di-mers and tetramers). The population of the donor- and acceptor-labeled species grows with time (also see Fig. S6 for the time-dependent histograms at three different final concentrations ofacceptor-labeled TD). The distributions were fitted to the sum ofa log-normal function (for the donor-only peak) and a two-component Gaussian function (details of the fitting procedurein Materials and Methods and SI Materials, Methods, and Theory,Measurement of Dimerization Kinetics and Dissociation Constantsof Dimer and Tetramer Using Two-Color FRET). The time-dependent relative fractions of the two Gaussian componentswere calculated and used in model fitting (Fig. 5C).To fit the oligomerization kinetics data, we related the frac-

tions of these two components to the concentrations of themonomer, dimer, and tetramer (details in Materials and Methodsand SI Materials, Methods, and Theory,Measurement of DimerizationKinetics and Dissociation Constants of Dimer and Tetramer UsingTwo-Color FRET). Due to the incomplete acceptor labeling and thepresence of inactive (or photobleached) acceptors, each componenthas contributions from different oligomeric species with a differentnumber of active acceptors as seen in the immobilization ex-periment (Fig. 4A). Therefore, we incorporated the acceptorlabeling efficiency (i.e., the fraction of the active acceptor) intothe model as an additional fitting parameter. The concentrationsof the oligomer species were found by solving differential kineticequations numerically (Eqs. S53 and S54). By fitting the exper-imentally determined fractions of the two components in thehistograms to those calculated using the model (solid curves inFig. 5C), we determined the dissociation constants and the dis-sociation rate of the dimer. The dissociation constants of thedimer and tetramer are 2.2 (± 0.4) nM and 1.8 (± 0.2) nM forA1-TD and 3.1 (± 0.5) nM and 1.0 (± 0.2) nM for TD-A1, re-spectively, and the dimer dissociation rate is 1.6 (± 0.2) h−1 forA1-TD and 2.0 (± 0.2) h−1 for TD-A1. These dissociation con-stants are similar to those obtained from the FCS measurement(Materials and Methods and SI Materials, Methods, and Theory,Determination of the Dimer and Tetramer Dissociation ConstantsUsing FCS Measurement and Fig. S7).

A

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C

Fig. 4. Photobleaching of the acceptors in the tetramer and characterizationof the dimer conformation in the two-color experiment. Trajectories showingtransitions in the FRET efficiency are shown in Fig. S4A. (A, Left) Transition mapconstructed from the FRET efficiencies before [E (initial)] and after [E (final)]transitions in the experiment with the immobilized donor-labeled TD in-cubated with 10 nM acceptor-labeled TD (TD-A1). (A, Right) The expected Evalues of the three clusters of the tetramer species with various active acceptorlabels (enclosed in black rectangles). The donor is attached to chain 1. All ofthe tetramer species with an active acceptor in chain 3 are aggregated in thepeak at E ∼ 0.8 regardless of the acceptor status of the other sites. (Additionaltransfer to the acceptor in chain 2 or 4 increases the FRET efficiency by only0.03.) The FRET efficiency of the tetramer with two active acceptors in chains2 and 4 is expected to be ∼0.5. The tetramers with a single active acceptor inchain 2 or 4 and the dimer are expected to appear at E ∼ 0.4. In A, Left, blueand green ellipses indicate the locations of the transitions between theseclusters above (dashed) and below (solid) the diagonal. (B) FRET efficiencyhistograms of the dimers constructed from the trajectories with a singleacceptor bleaching followed by donor bleaching. (B, Right) A small peak atE ∼ 0.8 for TD-A1 results from the tetramer with a single active acceptor inchain 3. (C) Two-dimensional FRET efficiency– donor lifetime plot of the data inB. FRET efficiencies and donor lifetimes were obtained as described in Fig. 3.

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Dimer Conformation Probed by Three-Color FRET Experiment. In thetwo-color experiments described above, only intermolecularFRET can be monitored for binding. Therefore, there is no di-rect information on the conformation of the monomer chain indifferent oligomeric states. However, the conformational dif-ference of the monomer chain can be probed by three-colorFRET. In a three-color FRET experiment, an immobilized TDmonomer (D-TD-A1) labeled with the donor (D, Alexa 488) andacceptor 1 (A1, Alexa 647) at the N and C termini is incubatedwith TD molecules labeled with acceptor 2 (A2, Alexa 750) atthe C terminus in solution (TD-A2, Fig. 2C). In this way, theintramolecular FRET between D and A1 on the same monomerchain is observed simultaneously with the intermolecular FRETfrom D to A2 or A1 to A2. Fig. 6A shows representative three-color trajectories. After determining E12 (between A1 and A2)from the trajectory with A1 excitation (Fig. 6A, Lower, 640 nm),E1 (between D and A1) and E2 (between D and A2) can becalculated using the trajectory with D excitation (Fig. 6A, Upper,485 nm) (SI Materials, Methods, and Theory, Calculation of FRETefficiencies in three-color FRET).However, as in the two-color experiment, many trajectories

miss one or two dyes due to incomplete labeling. When one dyeis missing, the experiment becomes a complex two-color one,because of various combinations of two dyes, as shown in Fig. 6B.According to the labeling positions of the three fluorophores inFig. 2, E2 and E12 correspond to the FRET efficiencies in thetwo-color experiments with A1-TD and TD-A1, respectively.Importantly, the consistency of the analysis is shown by the factthat both E12 and E2 distributions reproduce those of the two-color experiments. There are two peaks in the E12 histogram at10 nM of TD-A2 and the high-E peak disappears upon the ad-dition of 2.5 μM unlabeled TD. The transition map of E12 (Fig.S4D) is very similar to that of the two-color experiment with10 nM TD-A1 (Fig. 4A and Fig. S4B). The high-E2 component(E2 ∼ 0.4) also disappears after 2.5 μM of unlabeled TD is added(Fig. 6B) as in the case of the two-color experiment with A1-TD.In this comparison, instead of the true FRET efficiency E2, weuse E2′ without acceptor blinking correction because it is difficultto extract the acceptor bright-state population when E2 is verylow and similar to the value of the A2 dark state.The intramolecular energy transfer efficiency E1 provides addi-

tional important information. At 10 nM TD-A2, there are twopeaks at E ∼ 0.67 and 0.82 and the lower-E peak disappears after2.5 μM unlabeled TD is added (Fig. 6B). This result indicates thatE ∼ 0.82 is the FRET efficiency in the dimer and tetramer states asexpected from the short distance between N and C termini in thetetramer structure (Fig. 2A) and E ∼ 0.67 is the FRET efficiency ofthe monomer. This interpretation is supported by the two-colorexperiment of D-TD-A1 without TD-A2 (Fig. S8A). A singlepeak at E ∼ 0.67 is observed when no unlabeled protein is addedin the solution and this peak is shifted to E ∼ 0.82 by the additionof 2.5 μM unlabeled TD. The low FRET efficiency of 0.67 sug-gests that the monomer is unfolded (intrinsically disordered;Discussion). Indeed, a positive shift from the diagonal is observedin the 2D E1-donor lifetime plot (σc

2 = 0.06, Fig. S8D), indicatingconformational flexibility of the unfolded TD molecule.Fig. 6D shows the E1 and E12 distributions when all three dyes

are active. E1 is always high regardless of the addition of un-labeled TD because the detection of the three fluorophoresmeans that the dimer (or tetramer) is formed. The two peaks inthe E12 histogram are very similar to the results in Fig. 6B, inwhich Alexa 488 is absent, indicating no influence of Alexa

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trations were globally fitted as described in SI Materials, Methods, andTheory (solid curves) to obtain four parameters: the dissociation constants ofthe dimer (Kd

D) and tetramer (KdT), the acceptor-labeling efficiency (φ,

fraction of the active acceptor), and the dimer dissociation rate (kd). KdD =

2.2 (± 0.4) nM, KdT = 1.8 (± 0.2) nM, φ = 0.31 (± 0.01), and kd = 1.6 (± 0.2) h−1

for A1-TD and KdD = 3.1 (± 0.5) nM, Kd

T = 1.0 (± 0.2) nM, φ = 0.44 (± 0.03),and kd = 2.0 (± 0.2) h−1 for TD-A1.

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488 on the determination of E12. The unique feature of three-color FRET is its capability of determining all three FRETefficiencies simultaneously. It should be possible to find thecorrelation between the E12 values in the two peaks and theother two FRET efficiencies. For example, even though E1shows a single peak (Fig. 6D), there may be a difference betweenthe high- and low-E12 species (i.e., tetramer and dimer). How-ever, for the TD constructs in this work, E2 is too low (before γcorrection, E2 ∼ 0.1) to be determined accurately in the three-color experiment. (Although E2 is not accurate, its value is so lowthat E1 is reasonably accurate as shown in Fig. 6E, Top.) Instead,we avoided this problem by analyzing the segments that imme-diately follow photobleaching of A1 or A2. For example, in thetwo trajectories in Fig. 6A, Left, A2 photobleaches earlier thanA1. In the two trajectories in Fig. 6A, Right, A1 photobleachesearlier than A2. Because the dissociation/association kinetics arevery slow, the oligomeric state would be the same before andafter photobleaching of these dyes. Therefore, it is possible todetermine E1 and E2 more accurately using two-color segmentsafter photobleaching of A2 and A1, respectively, and correlatethese values with E12 in the preceding three-color segment. Fig.6E shows this analysis. E2 is low when E12 is low (Fig. 6E, BottomLeft) and E2 is high when E12 is high (Fig. 6E, Bottom Right).

(The number of trajectories for high E12 is very small becausephotobleaching of A1 earlier than A2 especially with high E12 isa very rare event.) The difference of E1 (Fig. 6E, Middle) is verysmall between the high- and low-E12 states, indicating that theaverage distances between N and C termini of a monomer chainin the dimer and tetramer states are similar (Fig. 7).

DiscussionWe have described two- and three-color single-molecule FRETexperiments and a fluorescence lifetime analysis and have shownhow to use these methods to characterize a specific oligomericstate in an equilibrium mixture that is not separable by ensemblemethods and is difficult even with single-molecule methods. Weperformed two-color experiments with two different TD con-structs having different labeling positions, in which the in-formation of the distances between the C terminus of one chainand the N (A1-TD) or C terminus (TD-A1) of the other chain ofthe dimer can be obtained. In principle, all this informationcould be obtained in a single three-color experiment, and weconfirmed that the results of the three-color experiment repro-duced the observations in the two-color experiments. However,due to various problems, such as incomplete dye labeling, and lowquantum yield and rapid photobleaching of the third fluorophore

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Fig. 6. Dimerization and tetramerization of TD probed by three-color FRET. Data were collected for immobilized Alexa 488- and Alexa 647-labeled TD (D-TD-A1) incubated with 10 nM Alexa 750-labeled TD (TD-A2). (A) Representative fluorescence trajectories (20-ms bin time) in the donor (D, Alexa 488), acceptor 1(A1, Alexa 647), and acceptor 2 (A2, Alexa 750) channels obtained by D excitation (485 nm, Upper panels) and A1 excitation (640 nm, Lower panels) (also seeFig. S9). Red and purple arrows indicate photobleaching of A1 and A2, respectively. (B–D) Mean FRET efficiencies and lifetimes were calculated from the initialsegment of the trajectories before (Left) and after (Right) the addition of 2.5 μM unlabeled TD. (B) E1, E2′, and E12 were calculated from the two-colorsegments that miss A2, A1, and D and contain more than 1,500, 1,000, and 1,000 photons, respectively. (C) Two-dimensional E1–donor lifetime plots of thedata in B. (D) E1 and E12 were obtained from the segments (>1,000 photons) in which all three dyes are active. (E) Distributions of E1 and E2′ constructed forthe low (Left)- and high (Right)-E12 species. FRET efficiencies were calculated from the segments with three active dyes (E1, Top) or from the two-colorsegments immediately following photobleaching of A2 (E1, Middle) or A1 (E2′, Bottom). All FRET efficiency and lifetime values were corrected as described inFig. 3 except E2′, which was not corrected for acceptor blinking.

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(Alexa 750), the results of the three-color experiment are complexand not as quantitative as those of the two-color experiments.Consequently, we focused on extracting information that can beuniquely obtained by a three-color experiment and demonstratedhow to combine this with more quantitative two-color results toderive structural and dynamical information for the various olig-omer conformations. We showed that corrections for acceptorblinking are essential for accurate determination of the FRETefficiency and donor lifetime, especially for the estimation of theconformational flexibility in the 2D E–lifetime analysis.The protein oligomerization system studied here is the tetra-

merization domain of the tumor suppressor protein p53. Becausean atomic-resolution structure is known for the tetramer (45–47), we focused on the characterization of the monomer anddimer. Our original strategy was to characterize the monomerand dimer at a low concentration where the tetramer does notexist. Therefore, it was initially puzzling to observe broad dis-tributions and multiple peaks in the FRET efficiency histograms(Fig. 3) and irreversible transitions between these states (Fig. 4).For the 42-residue peptide (residues 319–360 of full-length p53)used in this work, it turned out that the tetramer dissociationconstant is very low, similar to the dimer dissociation constant(Fig. 5 and Figs. S6 and S7), unlike a shorter 31-residue peptide(residues 325–355) and the full-length protein (49). Therefore,the tetramer with multiple acceptors coexists with the dimer atlow nanomolar concentrations, which explains the observedFRET efficiency distributions and the asymmetric transitionmaps. Although these features make the analysis more complex,it actually demonstrated the capability of combining two- andthree-color single-molecule FRET spectroscopic methods tocharacterize individual oligomeric species in a mixture. We alsoshowed that the slow dimerization kinetics can be measured by thefree diffusion experiment after manual mixing (Fig. 5 and Fig. S6).The monomer can be characterized relatively easily by

simply lowering the concentration until the dimer dissociates(<100 pM). In the two-color measurement of TD labeled withAlexa 488 and Alexa 647 at the N and C termini (D-TD-A1),the FRET efficiency for the monomer is 0.67 (Fig. S8A andTable S1). In addition, the 2D FRET efficiency–lifetimeanalysis shows a positive shift of the distribution from thediagonal. This shift results from a broad FRET efficiencydistribution (σc

2 = 0.06, Fig. S8D) reflecting the presence of

rapidly interconverting conformations with different donor–ac-ceptor distances (i.e., conformational flexibility). The low E value(0.67) compared with those of the dimer and tetramer states (0.82)and the flexibility of the monomer chain suggest that the monomeris unfolded, consistent with the result of the monomeric mutant(L344P) that does not form oligomers (59). Single-molecule dataof unfolded polypeptide chains have been well described bypolymer models (9) such as the Gaussian chain model (7, 41, 42,60–62), in which the end-to-end distance (r) distribution is givenby P(r) = 4πr2[3/(2π〈r2〉)]3/2exp[–3r2/(2〈r2〉)]. The great advan-tage of the Gaussian chain model is that there is only one freeparameter,〈r2〉, which can be determined from the experimen-tally obtained mean FRET efficiency as E=

R∞0 EðrÞPðrÞdr (Re-

sults). With the experimentally determined〈r2〉1/2 = 4.8 nm, thevariance of the Gaussian chain is σc

2 = 0.10, which is larger thanthe measured value of 0.06 (± 0.03). In other words, the chaindynamics are more restricted than expected from the Gaussianchain model. It has been known that intrinsically disorderedproteins behave like a random polymer even though they aremore collapsed compared with the proteins unfolded by chemicaldenaturant (9). Moreover, the end-to-end distance distribution doesnot depend much on the specific polymer model [σc

2 = 0.09 for theself-avoiding walk model (9)]. The narrower end-to-end distancedistribution may result from the unusually high fraction of thecharged residues (43%) in the sequence of the TD that mightcause less flexibility of the unfolded chain. However, the netcharge is 0 at neutral pH and the residues with opposite chargesare well mixed. In this case, the chain dynamics are not affectedby charges but resemble those of random polymers (63). There isa possibility that some residual secondary structure is formed inthe monomer state, but it is difficult to prove experimentally,because the TD will form tetramers at the concentrations nec-essary for high-resolution structural techniques.Two- and three-color binding experiments showed that the

structure of the monomer chain is similar in the dimer and tet-ramer states, but it is more flexible in the dimer state. Althoughthe solution is a mixture of the monomer, dimer, and tetramerat the concentration of 10 nM, in the two-color binding experi-ment, the selective detection of the dimer was made possible byanalyzing the trajectories exhibiting single-donor and single-acceptor photobleaching (with a small fraction of tetramers). Inboth cases of A1-TD and TD-A1, the FRET efficiencies in thedimer state (Fig. 4B) are higher than those in the tetramer state(Fig. 3B after adding excess unlabeled TD), suggesting moreflexibility in the dimer state, which may bring the two terminiclose to each other (Fig. 7). The flexibility of the chains moni-tored by the 2D FRET efficiency–lifetime analysis also supportsthis interpretation. The 2D distributions of the dimer and tet-ramer in Figs. 4C and 3C show that the width of the distancedistribution between the N terminus of one monomer chain andthe C terminus of the other chain in the dimer state is similar tothat in the tetramer state [σc

2 = 0.07 (± 0.02) and 0.05 (± 0.02)before and after the addition of the unlabeled TD in the A1-TDbinding experiment (Table S1)]. On the other hand, the distancedistribution between the two C termini in the tetramer [σc

2 =0.02 (± 0.02)] is much narrower than that in the dimer [σc

2 = 0.06(± 0.02)]. These two distinct results suggest that the C terminus ofthe chain is more flexible in the dimer state than in the tetramerstate whereas the flexibility of the N terminus is similar in both states,consistent with the previous NMR and simulation results (48, 56).This difference can be explained more clearly by the dimer

and tetramer structures (46) in Fig. 7. In the tetramer state, theα-helices form the core in the middle, sandwiched by theβ-strands outside. In fact, seven and five residues of the N and Ctermini (eight and six including the residues where dyes are at-tached), respectively, are unstructured, and this accounts for therelatively large variance of E even in the tetramer state. Especially,the acceptor at the N terminus (Fig. 7, Left) can access the regionclose to the donor side. This flexibility of the N terminus will besimilar in the dimer and the tetramer states, which results in thesimilar variance of the FRET efficiency in the A1-TD experiment.

Fig. 7. Average distance between dye labels and the flexibility of the N andC termini in the dimer and tetramer states. The size of the dashed arrowsindicates the relative flexibility of the donor (green)- and acceptor (red)-labeled termini. In the dimer state, both N and C termini are largely flexi-ble and the variance of the FRET efficiency distribution (σc

2) is relatively large(Figs. 3C and 4C and Table S1). In the tetramer state, the flexibility of the Cterminus is smaller (indicated by smaller arrows) because the lower part ofthe labeled dimer is blocked by the unlabeled dimer. Therefore, σc

2 of theFRET efficiency between C termini (TD-A1, Center) is small. On the otherhand, σc

2 of the tetramer with A1-TD (Left) is still large because the flexibilityof the acceptor-labeled N terminus will not be affected by the tetramerformation. The corrected FRET efficiencies, average distances (calculatedusing κ2 = 2/3), and σc

2 values obtained from the two- and three-color ex-periments are listed in Table S1.

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On the other hand, the C terminus is much more restricted in thetetramer state compared with the dimer state (Fig. 7, Center).Therefore, the variance of the FRET efficiency distribution inthe TD-A1 experiment is much smaller for the tetramer than forthe dimer. Several groups have recently developed tools to cal-culate an accurate distribution of the distance between the donorand acceptor by appropriate modeling of fluorophores andlinkers for macromolecules with well-defined structures (64–69). This calculation may allow for a more quantitativecomparison. However, as mentioned above, there is a fairamount of disorder in both N- and C-terminal regions of themonomer unit in both dimer and tetramer states. Therefore,more quantitative analysis and comparison would be possible inconjunction with molecular dynamics simulations.The above structural analysis is based on the assumption that

the conformation of the monomer chain is similar in the dimerand tetramer states, which is almost certain but cannot be provedby the two-color experiment alone. The three-color experimentprovides unambiguous and more complete information for thedimer conformation. We showed that the FRET efficiency dis-tributions of E2 and E12 are consistent with those of the two-color experiment with A1-TD and TD-A1, respectively. TheFRET efficiency E1 between the N and C termini of the samechain is high (∼0.82) in both the dimer and tetramer states,which clearly indicates that the structure (β-strand, turn, andα-helix) found in the tetramer is also present in the dimer state.In principle, three-color FRET experiments alone can extract

3D information of molecular structure and kinetics by measuringthree distances. In practice, however, various complicationscaused by introducing an additional dye make it difficult to ob-tain information with the same accuracy as in the two-color ex-periment. However, as we have demonstrated in this work, bycombining two- and three-color experiments it is possible toobtain 3D quantitative information with high accuracy. The ca-pability of selectively detecting specific oligomeric species will bevery useful in exploring other protein oligomerization systemsinvolved in important biological and disease processes.

Materials and MethodsMaterials. In the binding experiment, three different TD constructs were used(Fig. 2D). TD with a biotin tag and an unnatural amino acid, 4-acetylphenylala-nine (70, 71), at the N terminus (Avi-UA-TD-Cys) was labeled with Alexa 488 atthe C terminus (TD-D) for the two-color experiment. The same protein was site-specifically labeled with Alexa 488 and Alexa 647 at the N and C termini,respectively (D-TD-A1) for the three-color experiment. TDs with an addi-tional cysteine residue at the N (Cys-TD) or C terminus (TD-Cys) were labeledwith Alexa 647 (A1-TD or TD-A1) and Alexa 750 (TD-A2) for the two- and three-color experiments, respectively. Details of the expression, purification, and dyelabeling of proteins are described in SI Materials, Methods, and Theory.

Single-Molecule Spectroscopy. To determine the FRET efficiency and donorlifetime, TD-D (D-TD-A1) was immobilized and incubated with A1-TD or TD-A1(TD-A2) in the two-color (three-color) experiments. For the determination ofthe dissociation constants and the dimerization kinetics, TD-D was manuallymixed with A1-TD or TD-A1 and fluorescence bursts were collected in the freediffusion experiment. The dissociation constants were also determined usingequilibrium FCS measurement of the TD-D mixed with unlabeled TD (Cys-TD).

Among various corrections, the most complex step in the FRET efficiencydetermination is the acceptor blinking correction. In this step, first, the

population of the acceptor bright state (pb) was obtained using the maximum-likelihood method. With this population, the FRET efficiency corrected forblinking (Ec) in the two-color experiment can be calculated relatively easily asEc = E/pb (Eq. S29), where E is the FRET efficiency before the blinking correc-tion. In three-color FRET, there are four different combinations of the brightand dark states of the two acceptors. The photon count rates of these fourcases can be explicitly expressed in terms of three FRET efficiencies in theabsence of acceptor blinking (Eq. S34). The actual photon count rates in thepresence of acceptor blinking are linear combinations of these four cases withrelative weights determined by the bright-state populations of the two ac-ceptors (Eqs. S33 and S35). Then, the FRET efficiencies corrected for acceptorblinking can be found by solving Eqs. S36 and S37.

The donor fluorescence lifetime was determined using the mean delaytime (Eq. S19), which was subsequently corrected for background and ac-ceptor blinking. The origin of the delay time was determined by fitting thedelay time distribution (Eq. S20) obtained from donor-only trajectorieswithout the active acceptor.

Further details of single-molecule experiments, theories of two- and three-color FRET, lifetime determination, corrections of background, donor leak,γ-factor, direct acceptor excitation, and acceptor blinking (maximum-likelihood method) are described in SI Materials, Methods, and Theory.

Oligomerization Equilibrium and Kinetics. In this work, the oligomerizationkinetics of TD were measured by mixing donor-labeled TD with an excess ofacceptor-labeled TD in the free-diffusion experiment. Using the acceptor-labeling efficiency (the fraction of the active acceptor), the relative ampli-tudes of the components observed in FRET efficiency histograms (Eq. S51) wererelated to the concentrations of the donor-labeled species with an arbitrarynumber of acceptor labels (Eq. S52). There is only one donor-labeled TDmonomer in each oligomeric species because the concentration of the donor-labeled TD is much smaller than those of acceptor-labeled or unlabeled TD.

The concentrations of the donor-labeled species were found by numericallysolving the kinetic equations that couple the concentrations of monomers,dimers, and tetramers with and without donor labels (Eqs. S53 and S54).To simplify the kinetic equations, we assumed that the dimer–tetramerequilibration is much faster than the dimer–monomer equilibration (49).The similar growth rates of the two components (E > 0) at a given acceptor-labeled TD concentration support this assumption. There are four fittingparameters in the kinetic equations: the equilibrium dissociation constantsof the dimer and tetramer, the rate constant of dimer dissociation, and theacceptor labeling efficiency. Further details of the determination of thedissociation constants and dimerization kinetics are described in SI Materials,Methods, and Theory.

It should be noted that both the equilibrium constant and the kineticequation for a reaction between unlabeled (indistinguishable) moleculesdiffer from those between the labeled and unlabeled (distinguishable)molecules by a statistical factor. For example, the dissociation constant ofthe dimer of donor-labeled and unlabeled TD monomers is one-half of thedissociation constant of the dimer of unlabeled TDmonomers. As a result, therelative populations of the donor-labeled oligomers are different from thosewithout a donor label. This fact should be considered carefully in the analysis(SI Materials, Methods, and Theory, Oligomerization Equilibrium BetweenUnlabeled Molecules and Between Labeled and Unlabeled Molecules).

ACKNOWLEDGMENTS. We thank W. A. Eaton and A. Szabo for numeroushelpful discussions and comments; P. G. Schultz for sharing the plasmid forthe expression and incorporation of the unnatural amino acid, 4-acetylphe-nylalanine; and A. Aniana for technical assistance with protein expressionand purification. This work was supported by the Intramural ResearchProgram of the National Institute of Diabetes and Digestive and KidneyDiseases, NIH.

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