Strength in Numbers: Effects of Acceptor Abundance on FRET Efficiency

Reprint© Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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Table of Contents

�. I. F�bi�n, T. Rente, J. Szçllosi,L. M�tyus,* A. Jenei*

3713 – 3721

Strength in Numbers: Effects ofAcceptor Abundance on FRETEfficiency

Spectroscopic ruler for molecular dis-tances: Fluorescence resonance energytransfer (FRET) is a strongly distance-de-pendent process between a donor andan acceptor molecule which can be ex-ploited for studies in biological systems(see graph). Manipulation of fluoro-phore/protein ratios of conjugated anti-bodies has large impact on the transferefficiency and expands the potential ofFRET measurements.

DOI: 10.1002/cphc.201000568

Strength in Numbers: Effects of Acceptor Abundance onFRET Efficiency�kos I. F�bi�n,[a] T�nde Rente,[a] J�nos Szçllosi,[a, b] L�szl� M�tyus,*[a, b] and Attila Jenei*[a]

1. Introduction

Resonance energy transfer, originally described by Fçrster inthe 1940s, is a spatially limited dipole–dipole interaction be-tween a donor and an acceptor molecule.[1] During this processthe excitation energy of the donor is transferred to the accep-tor in a nonradiative way, resulting in simultaneous excitationof the acceptor and deexcitation of the donor. When both ac-ceptor and donor are fluorescent molecules, the energy trans-fer is referred to as fluorescence resonance energy transfer(FRET).[2] The rate of transfer shows strong distance depend-ence (it is inversely proportional to the sixth power of the dis-tance between acceptor and donor) which allows FRET mea-surements to be used as a spectroscopic ruler for assessingmolecular distances.[3–7] Energy transfer can be characterizedby the efficiency of the transfer, which gives the probability forthe donor excitation energy to be transferred to the acceptor.FRET measurement is a valuable tool for investigating biologi-cal processes at the molecular level, because interactions canbe imaged for distances far below the diffraction limit of con-ventional imaging techniques.[8–11]

FRET measurements have become widespread owing to therecent implementations for microscopic and flow cytometricsetups.[12–16] Measurements usually involve detecting thequenching of donor fluorescence in the presence of accep-tors[17, 18] or scaling of sensitized emission of the acceptor tototal unquenched donor intensity.[12, 19] There are also severalmethods that measure the fluorescence lifetime of thedonor[20, 21] or changes in the bleaching kinetics of the donorfluorescent signal caused by FRET.[13, 22, 23] FRET imaging tech-niques have also been successfully adapted for experimentswith fluorescent proteins.[24–28] High-throughput methodsbased on FRET detection are emerging as well.[29–33] AlthoughFRET measurements are mostly robust, several factors besidesmolecular distance can influence the measured transfer effi-

ciency.[34–38] Both instrument setup and the chosen experimen-tal method affect the noise and sensitivity of the measure-ment, while limited movement of fluorophores or the microen-vironment of the dyes (for instance nonfluorescent quenchers)directly influence FRET, that is, alter the value of measuredtransfer efficiency. These factors affect our capability to detectFRET and might be less important in semi-quantitative mea-surements where only a relative change (increase or decrease)is monitored, but are absolutely critical for precise distancemeasurements.

The effect of relative abundance of dyes on the FRET pro-cess is often overlooked. Multiple acceptors interacting withthe same donor increase the probability of FRET even withouta change in molecular distance and thus lead to a higher trans-fer efficiency.[34, 39–42] This effect is especially important in live-cell measurements[26] where natural distribution differencesand movement of proteins can influence the number of ac-ceptors interacting with a given donor. Herein, we first give abrief theoretical overview of FRET and of how the interactionof different amounts of donors and acceptors alter the mea-

Fluorescence resonance energy transfer (FRET) is a strongly dis-tance-dependent process between a donor and an acceptormolecule, which can be used for sensitive distance measure-ments and characterization of molecular interactions at thenanometer level. The original mathematical description of thisprocess, however, is only valid for the interaction of one donorwith one acceptor. This criterion is not always met, especiallyin biological systems, where multiple structures can interact si-multaneously, often making distance estimations based ontransfer efficiency values error-prone. Herein we investigate

how the interaction of multiple acceptors and donors influen-ces the transfer efficiency value in an intramolecular cellularFRET system by manipulating the fluorophore/protein ratio ofthe fluorophore-conjugated antibodies. We show that the la-beling ratio of the acceptor has the largest influence on mea-sured transfer efficiency and decreasing or increasing the ac-ceptor labeling ratio can be utilized to manipulate the FRET re-sponse of the acceptor–donor pair and therefore is a tool foroptimizing sensitivity of FRET measurements.

[a] Dr. �. I. F�bi�n, T. Rente, Prof. J. Szçllosi, Prof. L. M�tyus, Dr. A. JeneiDepartment of Biophysics and Cell BiologyUniversity of Debrecen98 Nagyerdei krt. H-4032 Debrecen (Hungary)Fax: (+ 36) 52-412-623E-mail : [email protected]

[email protected]

[b] Prof. J. Szçllosi, Prof. L. M�tyusCell Biology and Signaling Research Group of the Hungarian Academy ofSciencesResearch Centre for Molecular MedicineMedical and Health Science CenterUniversity of Debrecen98 Nagyerdei krt. H-4032 Debrecen (Hungary)

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sured FRET efficiency. We demonstrate experimentally the ef-fects of changing the donor and acceptor abundance by vary-ing antibody labeling ratios in an intramolecular FRET modelsystem. For our experiments the ErbB2 receptor, a member ofthe epidermal growth factor receptor family,[43] was labeledwith noncompeting antibodies, trastuzumab and pertuzu-mab,[44, 45] on NCI-N87 gastric tumor cells.[46] The two antibodiesbind to separate epitopes on the same protein, thereforewhen using whole antibodies, predominantly intramolecularFRET over a fixed distance can be measured.[19] Our measure-ments highlight the influence of acceptor availability on theFRET efficiency even when the molecular distance stays un-changed and show how experiments can be optimized for thebest sensitivity in FRET detection by varying the labeling ratioof the antibodies used.

2. Results and Discussion

2.1. Comparison of Different F/P Ratio Variants ofAntibodies

For our experiments trastuzumab and pertuzumab antibodieswere conjugated with Alexa Fluor 546, 555, and 647 dyes toyield antibodies with different fluorophore/protein labelingratios (L =F/P). We studied the effect of the F/P ratio of antibod-ies on the measured FRET efficiency because the F/P ratio canbe quite easily controlled to achieve desired changes in num-bers of interacting fluorophores. At the same time changing theF/P ratio does not influence biological behavior (that is, labelingwith different F/P ratio variants of the same antibody has thesame biological effect). Thus, any differences in the results willmostly be a consequence of differences in F/P ratios and not ofsome other, uncontrollable biological factor. Cell surface FRETexperiments were performed by labeling ErbB2 receptors over-expressed on NCI-N87 cells.[47] Furthermore, when using wholeantibodies of trastuzumab and pertuzumab, the ErbB2 systemcan be regarded as a primarily fixed-distance intramolecularsystem,[19] therefore FRET efficiency changes can be attributedto changes in the antibody F/P ratio.

Labeling ratios of dye-conjugated antibodies were verifiedby measuring the mean intensities of cells labeled with differ-ent F/P-ratio antibodies. Although the mean intensity in-creased with increasing F/P ratio, the intensity increase wasnot linearly proportional to F/P, especially not at higher F/Pratios (Figure 1 A). Further, the intensity curves plotted as afunction of antibody F/P ratios were similar for different anti-bodies conjugated with the same fluorescent dye and weredifferent for the same antibodies conjugated with differentdyes (data not shown). Saturation can already be present atF/P ratios as low as 2 (in the case of Alexa Fluor 546) and be-comes more prominent at higher F/P ratios. Intensity satura-tion curves plotted as a function of antibody concentration didnot differ for antibodies with different labeling ratios (Fig-ure 1 B), indicating that antigen recognition and binding of an-tibodies were not influenced by the labeling ratio. In otherwords, fluorophore conjugation did not alter the binding affini-ty of the antibodies.

To investigate whether binding to the cell surface can influ-ence the optical properties of the fluorophore-conjugated anti-bodies, flow cytometric measurements were complementedwith spectrofluorimetric studies. The emission and excitationspectra of fluorophore-conjugated antibody solutions were re-corded to rule out the possibility of a spectral shift due to anincreasing F/P ratio. This shift relative to fixed-bandwidth emis-sion and excitation filters would result in an unequal intensity-clipping for different antibodies, resulting in a drop-off of thesignal and thus mimics saturation. The recorded curves did notshow a shift in either the excitation or emission spectra (datanot shown). Absorption spectra also did not show significantdifferences between different F/P variants of fluorophore-con-

Figure 1. Dependence of fluorescence intensity on antibody labeling ratio.A) Intensity saturation as a function of antibody labeling ratio for NCI-N87cells labeled with different fluorophores conjugated to trastuzumab. B) In-tensity saturation as a function of antibody labeling concentration for NCI-N87 cells labeled with different F/P ratio variants of Alexa Fluor 546 conju-gated trastuzumab. C) Intensity saturation as a function of antibody labelingratio for Alexa Fluor 546 conjugated trastuzumab measured in solution byspectrofluorimetry and for labeled NCI-N87 cells by flow cytometry. Normal-ized intensity: Intensity values normalized to maximum intensity value de-termined from nonlinear curve fit.

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L. M�tyus, A. Jenei et al.

jugated antibodies (data not shown). After correcting for con-centration differences of the antibody solutions (different dilu-tions were used to keep solution absorbance below 0.05 tominimize inner filter effects), intensity saturation was still evi-dent and showed differences between the different fluoro-phores. The saturation of intensity as a function of antibodyF/P ratio observed with the spectrofluorimeter for free anti-bodies in solution was similar to the intensity curve of thesame antibody bound to the cell surface (Figure 1 C).

Anisotropy of antibody solutions was also measured to char-acterize the interaction of individual dyes bound to the sameantibody. Because the anisotropy showed a linear concentra-tion dependence similar to concentration depolarization offree dyes,[48] the anisotropy was measured at several concentra-tions and then plotted as a function of concentration (Fig-ure 2 A). The individual data points of a given antibody werelinearly fitted. The y-intercept (corresponding to the anisotropyof an infinitely dilute antibody solution and thus equal to theanisotropy of a single antibody without the perturbing con-centration effects), designated as the intrinsic anisotropy, wasused to compare the different F/P ratio variants of a given anti-body. We found that the intrinsic anisotropy decreased as theF/P ratio increased and that it was substantially higher thanthe anisotropy of the free dye (likely the result of slower rota-tion due to the bound antibody). This change of anisotropy asa function of F/P ratio was true for all antibodies used. Howev-er, the curves were characteristic for each of the fluorophoresinvestigated (Figure 2 B).

From our results we deduce that intensity quenching is notcaused by changes in the interaction of the labeled antibodieswith cellular antigens, since concentration-dependent satura-tion curves of different F/P ratio antibodies did not show sig-nificant differences and spectrofluorimetric measurementsshowed that free antibodies in solution display the same F/P-dependent intensity saturation which can be seen after cell la-beling. Both the F/P-ratio-dependent decrease in anisotropyand the intensity saturation as a function of antibody F/P ratiowere dye-specific, showed large inter-dye variation, but werenot influenced in any significant manner by the type of labeledantibody. This implies that presumably dye-specific, structure-dependent factors determine the nature of intensity quench-ing for a given dye.

2.2. Effect of Donor and Acceptor Abundance on MeasuredFRET Efficiency

Although FRET measurement is a powerful tool for viewingmolecular interactions at the nanometer level,[49, 50] interpretingFRET efficiency values and their changes can be a dauntingtask, especially when considering the inherent variability ofbiological systems. The relationship between FRET efficiencyand molecular distance seems straightforward. The critical Fçr-ster distance and therefore the efficiency measured at a givenmolecular distance depends on the intrinsic spectral propertiesand orientations of the donor and acceptor dyes. Biologicalsystems complicate this scenario because the original descrip-tion of FRET was intended for the interaction of one acceptorwith one donor.[34, 51] In cellular systems, however, the numberof fluorophores involved in FRET is usually not restricted totwo molecules. This can be a result of preexistent uneven pro-tein patterns and distributions or dynamic rearrangements aris-ing from complex formation, protein translocations, or simplelateral diffusion in the membrane.[52–55]

Under these circumstances the average rate of transfer forthe acceptor–donor system can change even without any un-derlying distance changes if the number of dyes participatingin the FRET process changes.[42] Increasing the number of ac-ceptors interacting with a given donor increases the probabili-ty of an excited donor to find an acceptor partner before deex-citation and leads to an increase in the rate of transfer andsubsequently in the transfer efficiency. If all n acceptors inter-acting with the donor are identical in terms of FRET interactionprobability, then the system’s rate of transfer will be n timesthe rate of transfer for one acceptor.[56, 57] In this case the rela-tionship between E0 (the original energy transfer efficiencywith one acceptor) and En (transfer efficiency after an n-fold in-crease in the rate of transfer) is given by Equation (1):

En¼nktransfer

nktransfer þ kother

¼ nktransfer

ktransfer þ kother

�ktransfer þ kother þ ðn� 1Þktransfer

ktransfer þ kother

¼ nE0

1þ ðn� 1ÞE0

ð1ÞFigure 2. Anisotropy of fluorophore-conjugated antibodies in solution.A) Anisotropy of different F/P ratio variants of trastuzumab conjugated withAlexa Fluor 546. B) Intrinsic anisotropy of trastuzumab conjugated witheither Alexa Fluor 546, Alexa Fluor 555, or Alexa Fluor 647 as a function ofantibody F/P ratio.

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Acceptor Abundance and FRET Efficiency

The above term can be linearized if the term A = E/(1�E) isused instead of E [Eqs. (2) and (3)]:

A0 ¼E0

1� E0ð2Þ

An ¼En

1� En¼ n

E0

1� E0¼ nA0 ð3Þ

Therefore, an increase in the rate of transfer from an initialvalue will result in a nonlinear increase in transfer efficiencywith a linear increase in E/(1�E) (Figures 3 A,B). Plotting A as afunction of the increase in the rate of transfer should yield aline that has a y-intercept at A = 0 and a slope of A0. The valueof A0 can be used to calculate E0 based on Equation (2), which,as the transfer efficiency between a single donor and its singleacceptor partner, can be used for distance calculations accord-ing to the original Fçrster equations [also see Eqs. (11)–(14) inthe Experimental and Computational Section for a detailed ex-planation of E0] .

Increasing the number of donor dyes does not increase theprobability of an individual donor to interact with an acceptor(although an individual acceptor interacts with more donordyes) and so the fraction of donor molecules losing the ab-sorbed energy through FRET does not change and the transferefficiency stays the same. Multiple donors interacting with anacceptor should not affect the transfer efficiency negatively,because donor deexcitation is so fast that the chance of two

simultaneously excited donors competing for the same accep-tor is minimal. Competition between donors would only be aproblem if the dye system could be driven into saturation witha high enough flux of exciting photons. However, at such ahigh photon flux, photobleaching would be prominent, ren-dering FRET measurements impractical. Therefore, under con-ventional circumstances, systems with multiple donors withininteraction distance of the same acceptor (such as antibodieslabeled with multiple dyes) can be regarded as a single donorsystem with respect to transfer probability.

To support our theory, cell surface measurements were car-ried out with the donor (Alexa Fluor 546 or Alexa Fluor 555)conjugated to pertuzumab and the acceptor (Alexa Fluor 647)conjugated to trastuzumab as well as with donor-conjugatedtrastuzumab and acceptor-conjugated pertuzumab. Measure-ments of both combinations yielded similar transfer efficiencyvalues, so for simplicity we only discuss results obtained withdonor-conjugated pertuzumab and acceptor-conjugated tras-tuzumab. Transfer efficiency for a given donor increased nonli-nearly with the increase of acceptor F/P ratio and followed theFRET saturation curve predicted by our theoretical calculations(Figures 4 A,B). All donors had similar saturation curves, howev-er we observed a shift of the curve towards higher transfer effi-ciency values with the increase of donor labeling ratios in thecase of Alexa Fluor 546. The transfer efficiency measured withdifferent F/P ratio variants of the same donor and any givenacceptor did not decrease with increasing donor F/P ratios, in-dicating that the FRET system was not driven into saturationand competition between excited donors for available accep-tors was not significant. The correlation between donor F/Pratio and transfer efficiency was weak, with a calculated Pear-son’s correlation coefficient of 0.14 for Alexa Fluor 546 and0.038 for Alexa Fluor 555, with the measured transfer efficiencyvalues between the same acceptor and increasing F/P variantsof a given donor showing only minor increases. On the otherhand, increasing the acceptor F/P ratio drastically increasedthe transfer efficiency with any given donor. The correlationbetween acceptor F/P ratio and transfer efficiency was strong,with a Pearson’s correlation coefficient of 0.95 calculated for allacceptor–donor combinations. We also examined whether theacceptor/donor (A/D) ratio influences the transfer efficiency.We found that the same A/D ratio can result in very differenttransfer efficiency values depending on the individual F/P ratioof the acceptor, and very similar transfer efficiencies can bemeasured with different A/D ratios if the F/P ratio of the ac-ceptor is the same (data not shown). Therefore we concludethat the A/D ratio on its own is not a determinant of the mea-sured transfer efficiency.

Next, we plotted E/(1�E) as a function of acceptor F/P ratio(Figures 4 C,D). The points from a given donor were fitted witha line with an A = 0 intercept. The linear fit was possible forboth donor dyes. The slope of the line increased with the in-crease of donor F/P, but this effect was more evident withAlexa Fluor 546 than with Alexa Fluor 555. As discussed previ-ously, the slope of each line can be used to calculate the char-acteristic E0 transfer efficiency for every donor. The characteris-tic transfer efficiency exhibited a linear dependence on the F/P

Figure 3. Effect of the rate constant on energy transfer efficiency. A) Energytransfer efficiency as a function of the rate constant. B) The same data wereplotted as A = E/(1�E) as a function of the rate constant. During the simula-tion only ktransfer was changed, all other deexcitation processes remained un-changed. E0 : initial transfer efficiency measured with arbitrary initial rate oftransfer.



ratio of the donor, with a larger influence of F/P ratio in thecase of Alexa Fluor 546 (Figure 4 E).

Our results show that the labeling ratio of the acceptor isthe most important determinant of the absolute value of trans-fer efficiency. The fact that plotting E/(1�E) as a function ofthe acceptor labeling ratio yields a line demonstrates that eachacceptor dye behaves similarly, increasing the probability ofFRET interaction to the same extent. Our transfer efficiencycurves as a function of acceptor F/P ratio also closely resemblepreviously published curves for varying concentrations of dyesrandomly distributed in solution,[51] further supporting ourtheory that acceptors bound to a single antibody have a non-preferential, equal chance to interact with the same donor.While our measurements prove acceptor availability as a limit-

ing factor for measured FRET efficiency, they show at the sametime that manipulating antibody labeling ratios can be asimple tool for increasing measurement sensitivity beyond abetter signal/noise ratio of the measured intensities. Based onour results, R0 of the acceptor–donor dye system can be ma-nipulated by changing the labeling ratios. If we denote Rn asthe Fçrster distance for a FRET system with n acceptors, thenby substituting Equation (14) into Equation (10) [see the Exper-imental and Computational Section], the relationship betweenRn and R0 is [Eqs. (4) and (5)]:

En ¼nR6

0

nR60 þ R6 ¼

R6n

R6n þ R6

ð4Þ

Figure 4. Dependence of FRET efficiency on antibody labeling ratio. A) and B) FRET efficiency was measured between A) Alexa Fluor 546 or B) Alexa Fluor 555conjugated pertuzumab (serving as donors) and Alexa Fluor 647 conjugated trastuzumab (serving as acceptor) and plotted against the labeling ratio of theacceptor. C) and D) The same data plotted as A = E/(1�E) against the acceptor labeling ratio. E) The characteristic transfer efficiency was plotted as a functionof donor labeling ratio for Alexa Fluor 546 and Alexa Fluor 555 fluorophores. Characteristic transfer efficiency: FRET efficiency measured with an acceptor la-beling ratio of 1.



Rn ¼ n16R0 ð5Þ

Although this does not seem like a significant increase in R0,it still leaves much room for manipulation of the FRET system(Figure 5). Simply by changing R0 of the system we can shift

the intermolecular distance–FRET response curve. Therefore, byincreasing the acceptor labeling ratio, the value of FRET effi-ciency can be increased. This can be useful in low-FRET sys-tems, where FRET levels can be elevated to levels detectableabove the background. Further, the curve can be shifted sothat all possible distance changes in a given system are fol-lowed by a significant change in FRET. For instance, reducingthe acceptor F/P ratio can be beneficial if FRET values are closeto saturation, since a smaller F/P ratio of the acceptor reducesR0 of the system and increases the FRET change over that par-ticular distance range. The benefit of this approach is thatFRET sensitivity is increased without having to choose a newacceptor–donor pair, which would involve remeasuring the efrcoefficient, recalculating R0, and reoptimizing the measurementsetup for the new dyes, if it is at all possible (e.g. , availabilityof different excitation wavelengths in a laser is limited, avail-able emission filters, etc.).

2.3. Impact of Homo-FRET between Donors on Hetero-FRET

Theoretically the donor F/P ratio should not influence the mea-sured FRET efficiency. However, we still saw a slight increase oftransfer efficiency from the increase in the donor F/P ratio,which was especially evident with Alexa Fluor 546 as donor.This effect is most likely caused by increasing homo-FRET be-tween the donor dyes upon increasing the number of dyesbound to the antibody. Homo-FRET is a FRET process whereboth donor and acceptor belong to the same dye species andit is possible because of the overlap between emission and ex-citation spectra of any given dye. The effect of homo-FRET can

be explained as follows. As the donor and acceptor movethrough their possible spatial positions, the relative orientationof the donor emission and acceptor excitation dipoles alsoconstantly changes, cycling from relative orientations favoringFRET transition to ones that preclude it.[58] This orientation istaken into consideration with the k2 parameter in the equationfor R0. The value of k2 is an averaged value for all the possibleorientations. From the donor’s standpoint this means that incertain positions k2 is large and FRET is likely [large rate oftransfer, see Eqs. (12) and (13)] and therefore dominates otherdeexcitation processes, such as fluorescence. In other positionsk2 is small and FRET transitions are not likely (small rate oftransfer), therefore other deexcitation processes determine thefate of the excited state. In our proposed model homo-FRETacts as a lifeline for the excited state in positions where k2 issmall and deexcitation would take place without a contribu-tion from FRET. Instead of non-FRET deexcitation, the donor’sexcited state can be conserved and transferred by homo-FRETto positions that favor FRET. One could argue that homo-FRETwill also “steal” the excited state from positions where FRET islikely. However, it has been shown that the number of possibleorientations where k2 is maximal is fewer than the number oforientations, where k2 is minimal (this is also reflected in theaveraged value of 2/3 for k2, which is closer to the theoreticalminimum of 0, than to the theoretical maximum of 4).[58] It fol-lows that homo-FRET is more likely from low k2 positions,since the excited donor spends more time in these positions.In short, homo-FRET, by transferring energy from positionswhere FRET has negligible probability increases the average ofk2, which results in a larger R0 and larger FRET efficiency with-out a decrease in acceptor–donor distance.

Spectrofluorimetric anisotropy measurements with free, fluo-rophore-conjugated antibodies in solution can give indirectproof for this hypothesis. The measured anisotropy is influ-enced by the type of interaction between the dyes bound tothe antibody. Collision quenching, for instance, shortens thefluorescence lifetime[59] and causes an increase in measuredanisotropy. On the other hand, diversification of emitted lightdirections caused by homo-FRET should reduce anisotropy.[60–62]

Our measurements show that increasing the F/P ratio reducesthe anisotropy in a dye-specific manner (see also Figure 2),which suggests that homo-FRET is the dominant underlyingprocess. Interestingly, the minimal value of intrinsic anisotropyis correlated with the F/P-ratio-dependent quenching of the in-tensity exhibited by an antibody, that is, the larger the intensi-ty saturation of an antibody, the higher the plateau value of in-trinsic anisotropy. This is in line with the assumption that in-tensity saturation is a consequence of collision quenching.Therefore, larger saturation means more quenching which cancounteract the effects of homo-FRET.

2.4. Implications for FRET Stoichiometry Measurements

FRET stoichiometry measurement[63] is a developing field thatwas born from the realization that most FRET measurementtechniques involve the recording of apparent transfer efficien-cies. This apparent FRET signal is a consequence of the inher-

Figure 5. Simulated distance–FRET response curves. Theoretical curves showthe FRET efficiency differences for intermolecular distances of 7 and 8 nmwhen measured with acceptor F/P = 1 (DE0) and acceptor F/P = 5 (DEn) withR0 = 4 nm.



ent signal averaging in FRET measurement methods, that is,even the smallest resolution unit (be it a cell in the flow cy-tometer or a pixel in a microscope image) in FRET experimentshas a signal averaged from multiple fluorophores within theresolution unit. In this way, signals from interacting and nonin-teracting fluorophore populations all contribute to emissionprofiles of acceptors and donors. The stoichiometry methodswork around this problem by utilizing a calibration standard,that is, the FRET efficiency for the used fluorophore pair ismeasured with a standardized construct containing one donorand one acceptor (the ratio of which we also advocate as nec-essary for absolute distance measurements) interacting at adistance characteristic for the system studied (this would beanalogous with our term E0). The fraction of interacting fluoro-phores (stoichiometry) is then calculated from the apparentFRET signal in the knowledge that actual FRET between donorand acceptor is equal to the characteristic FRET obtained withthe calibration construct.[64]

FRET stoichiometry measurements therefore have the pre-requisite that despite changing interacting fractions, the FRETprocess involves one donor and one acceptor with a constantFRET interaction and changes in apparent FRET are due tochanges in the proportion of averaged signals. This criterion ismet when the interaction is restricted to two molecules (e.g. ,receptor–ligand binding). Our experiments show that whenmultiple interaction partners are permitted in the FRET pro-cess, a change in interacting fractions can alter the molecularlevel FRET (a shift from E0 to En in our terminology). Underthese circumstances FRET stoichiometry cannot accuratelymeasure the total fraction of donors and acceptors participat-ing in FRET. Also, changes in the number of acceptors interact-ing with donors in a given FRET process will not be revealed.In these situations a lifetime-imaging approach is recommend-ed.[65]

3. Conclusions

The abundance of acceptors is a double-edged sword.Changes in acceptor F/P ratios can cause substantial shifts intransfer efficiency and this effect has to be considered whencomparing FRET results. It also has the consequence that FRETvalues cannot be directly converted into absolute distancevalues if antibody labeling ratios are higher than one. Instead,some kind of calibration has to be performed (either withmeasurements of known distances or calibration curves) priorto the conversion to distances. In a more general sense, to in-terpret FRET changes as a change in acceptor–donor distance,a change in the number of acceptors interacting with a donorhas to be ruled out.

The impact of acceptors on FRET efficiency can also be usedby researchers to their advantage. Manipulation of the Fçrsterdistance of a dye system is a valuable tool. The choice of a dyefor a FRET experiment is mostly influenced by the excitationand detection capabilities of the instruments used for themeasurements. This does not guarantee that the R0 value ofthe dye pair will allow FRET detection or result in sensitiveFRET changes for the distances encountered by donors and ac-

ceptors during the experiment. By changing the acceptor F/Pratio, the dye pair that works best with the measurementsetup can be fine-tuned to the needs of the given experimen-tal system, ensuring increased FRET response to distancechanges. Manipulation of antibody labeling ratios expands thepotential of FRET measurements, because we are no longerconfined to passively registering the inherent FRET of a givensystem, but instead can actively adapt our measurements toyield the best possible sensitivity and results.

Experimental and Computational Section

Experimental Details

Cell Line: NCI-N87 (American Type Culture Collection, Rockville,MD), a gastric adenocarcinoma cell line was chosen because thesecells express high amounts of ErbB2 on the cell surface. Cells weregrown in RPMI medium containing heat-inactivated fetal calfserum (10 %), l-glutamine (2 mm), and gentamicin (50 mg mL�1) inhumidified air containing CO2 (5 %) at 37 8C to subconfluency. Forflow cytometric measurements cells were harvested by treatmentwith trypsin (0.05 %) and ethylenediaminetetraacetic acid (0.02 %)before antibody labeling.

Conjugation of Antibodies with Fluorescent Dyes: The followingmonoclonal antibodies (mAbs) against ErbB2 were used: pertuzu-mab (gift from Hoffman-La Roche, Grenzach-Wyhlen, Germany)and trastuzumab (Hoffman-La Roche, Grenzach-Wyhlen, Germany).Antibodies were conjugated with fluorescent dyes according tothe manufacturers’ specifications. Briefly, covalent binding of themonofunctional succinimidyl ester derivates of amine-reactive dyes(Alexa Fluor 546, Alexa Fluor 555, and Alexa Fluor 647; MolecularProbes/Invitrogen, Eugene, OR) to the lysyl-e amino groups of anti-bodies was carried out in sodium bicarbonate buffer (0.1 m) atpH 8.3. Dyes dissolved in sodium bicarbonate buffer were addedto antibody solutions and the reaction mixture was incubated. Toobtain different fluorophore/protein (F/P) ratios of the antibodieswe changed antibody concentration, pH, or labeling time.Unreacted dye molecules were removed by gel filtration through aSephadex G-50 column. The F/P labeling ratio was determinedfrom absorption at 280 nm and the maximum absorption wave-length of the used dye by spectrophotometry (Nanodrop, Wilming-ton, DE) and was in the range of 1–10 for whole mAbs. To preventartifacts, we removed aggregates of dye-conjugated mAbs by cen-trifuging with 110 000 g at 4 8C for 20 min in an Airfuge ultracentri-fuge (Beckman Coulter, Fullerton, CA) prior to cell labeling.

Labeling of Cells with Fluorescent Antibodies: Freshly harvestedcells were washed twice in ice-cold PBS buffer (0.15 m NaCl,3.2 mm KCl, 8.7 mm Na2HPO4·12 H2O, 1.7 mm KH2PO4) at pH 7.4.The cell pellet was suspended in PBS at a final concentration of1 � 106 cells in PBS (50 mL) and cells were incubated with AlexaFluor 546, 555, or 647 conjugated mAbs alone on ice (4 8C) for30 min in the dark. The same procedure was used for FRET samplesin which a mixture of donor- and acceptor-conjugated antibodieswas added to the cell suspension. The excess antibody concentra-tion was at least fivefold above saturating concentration (final la-beling concentration of 100 mg mL�1) during the incubation. There-after cells were washed twice in PBS and fixed in 500 mL formalde-hyde/PBS (2 %). During labeling, special care was taken to keep thecells at ice-cold temperature to avoid induced aggregation of cellsurface molecules.



Anisotropy Measurements: Fluorescence anisotropy measurementswere performed on a Fluorolog-3 spectrofluorimeter (Horiba JobinYvon, Longjumeau, France). The excitation light was provided by a450 W Xe arc lamp. Anisotropy of Alexa Fluor 546, 555, and 647conjugated trastuzumab, free dye solutions, and PBS solution weremeasured with FL-1044 polarizers in l-format configuration. Theconcentration of the fluorescent-dye-conjugated antibodies andfree dyes were in the range of (1–10) � 10�6

m, where absorption ofthe sample was below 0.05 to ensure negligible inner filter effects.A 1 cm optical pathlength quartz cuvette (Hellma, M�llheim, Ger-many) was used. Excitation and emission monochromator wave-lengths were set according to emission and excitation maxima ofthe dyes applied. Slit width and acquisition time were chosen sothat all polarizer mode intensities (IVV, IVH, IHH, and IHV) for all concen-trations remained below 1 000 000 counts per second. Data was an-alyzed with DataMax for Windows v2.1 software.

Flow Cytometry Measurements: Flow cytometric energy transfermeasurements were carried out on a FACSArray bioanalyzer(Becton Dickinson, Franklin Lakes, NJ). The flow cytometer wasequipped with a 532 nm solid-state laser and a 635 nm diode laser.For FRET measurements the detectors with 585/42 band pass(donor channel), 685 long pass (energy transfer channel), and661/16 band pass (acceptor channel) filters were used. For everysample 20 000 events were acquired.

Computational Methods

FRET Calculations: FRET calculations were performed in a cell-by-cell manner after gating debris using custom-developed calcula-tion software, ReFlex (available at http://www.freewebs.com/cyto-flex). We used an intensity-based approach described in detail inrefs. [12, 19, 66]. Briefly, three different intensity channels were re-corded for each sample: I1, excitation at donor wavelength and de-tection at donor emission wavelength (donor channel) ; I2, excita-tion at donor wavelength and detection at acceptor emissionwavelength (energy transfer channel) ; I3, excitation at acceptorwavelength and detection at acceptor emission wavelength (ac-ceptor channel). With these three intensities the following initialequation set can be given [Eqs. (6)–(8)]:

I1 ¼ IDð1� EÞ þ IAS4 þS4

S2IDEa ð6Þ

I2 ¼ IDð1� EÞS1 þ IAS2 þ IDEa ð7Þ

I3 ¼ IDð1� EÞS3 þ IA þS3

S1IDEa ð8Þ

where ID and IA are the unquenched donor intensity and the pureacceptor intensity, respectively. E is the transfer efficiency, S1–S4 arecorrection factors for cross-excitation and spectral spillover deter-mined from donor- and acceptor-only labeled samples, and a is ascaling factor correcting for the difference in detectability of excit-ed donor and acceptor fluorophores. The factor a is determinedempirically according to Equation (9):

a ¼ IA2

ID1

LDBDeD

LABAeA

ð9Þ

where IA2 is the I2 signal of the acceptor-only labeled sample and ID

1

is the I1 signal of the donor-only labeled sample. L is the labelingratio of the antibodies, B is the mean number of receptors labeled,and e is the molar extinction coefficient of the dyes at the donor

excitation wavelength (the indices D and A refer to donor and ac-ceptor, respectively). The ratio of molar extinction coefficients ofthe fluorophores at the donor’s excitation wavelength (eD/eA) is theefr coefficient.In our experimental setups, S3 and S4 were negligible, thus allowingsimplification of the calculations, giving Equation (10) for the FRETefficiency:

A ¼ E1� E

¼ 1a

I2 � I1S1 � I3S2

I1ð10Þ

For each experiment, donor- and acceptor-only labeled specimensfor all applied F/P variants were measured and used to calculate Sfactors. S1 factors showed only small fluctuations corresponding tomeasurement noise over the viewed F/P range and therefore anaveraged value was used for FRET calculations, whereas S2 factorswere individually substituted with the value measured for a specif-ic acceptor labeling ratio. Transfer efficiency values are given asthe median values of normally distributed, unimodal energy trans-fer histograms for every sample.

Theory of FRET: To determine the effect of donor and acceptorabundance on the FRET efficiency, we first summarize the theory ofFRET. FRET is a nonradiative energy transfer process between anexcited donor and an adequately oriented acceptor molecule. Ingeneral, the FRET efficiency (E) is measured, which is defined as theratio of energy transfer to total donor deexcitation and can bewritten as Equation (11):

E ¼ ktransfer

ktransfer þ kother

ð11Þ

where ktransfer is the rate of transfer and kother is the sum of the rateconstants of all other deexcitation processes. The rate of transfer isdetermined by the distance between the donor and the acceptor[Eq. (12)]:

ktransfer ¼ kother

R60

R6ð12Þ

where R is the distance between the acceptor and the donor andR0 is the Fçrster distance. The Fçrster distance is characteristic forthe given donor and acceptor dye and can be calculated by Equa-tion (13):

R0 ¼ 978ðQDk2n�4JDAÞ1=6 ð13Þ

where QD is the donor quantum yield in the absence of acceptordyes. k2 is an orientation factor (its value can range from 0 to 4and is 2/3 for dynamically averaged isotropic transition moments).n is the refraction index of the conveying medium and JDA is thespectral overlap integral of the donor emission and acceptor exci-tation spectra. After combining Equations (11) and (12), the dis-tance dependence of the transfer efficiency is described by Equa-tion (14):

E ¼ 1

1þ R6=R60

� � ð14Þ

Therefore, R0, the Fçrster distance corresponds to the distancewhere the transfer efficiency is fifty percent. The nonlinear relationbetween FRET efficiency and donor–acceptor distance means thatthe transfer efficiency is sensitive to distance changes over a given



range. However, beyond this range it only changes slightly uponincrease or decrease of the distance.[49]

Acknowledgements

This work was supported by the T�MOP 4.2.1./B-09/1/KONV-2010-0007 project. (The project is implemented by the New Hun-gary Development Plan, co-financed by the European SocialFund.) It was also supported by the Hungarian Scientific ResearchFund (K77600 and K68763), by the Hungarian National Develop-ment Agency (TAMOP-4.2.2-08/1-2008-19), and by the EuropeanCommission (LSHC-CT-2005-018914, MCRTN-CT-2006-035946-2).

Keywords: antibodies · cell surface receptors · flowcytometry · fluorescence · resonance energy transfer

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Received: July 14, 2010Revised: August 31, 2010Published online on October 8, 2010



Strength in Numbers: Effects of Acceptor Abundance on FRET Efficiency

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