The Effect of Fluorophore Conjugation on Antibody Affinity and the Photophysical Properties of Dyes

Abstract

Because the degree of labeling (DOL) of cell-bound antibodies, often required in quantitative fluorescence measurements, is largely unknown, we investigated the effect of labeling with two different fluorophores (AlexaFluor546, AlexaFluor647) in a systematic way using antibody stock solutions with different DOLs. Here, we show that the mean DOL of the cell-bound antibody fraction is lower than that of the stock using single molecule fluorescence measurements. The effect is so pronounced that the mean DOL levels off at approximately two fluorophores/IgG for some antibodies. We developed a method for comparing the average DOL of antibody stocks to that of the isolated, cell-bound fraction based on fluorescence anisotropy measurements confirming the aforementioned conclusions. We created a model in which individual antibody species with different DOLs, present in an antibody stock solution, were assumed to have distinct affinities and quantum yields. The model calculations confirmed that a calibration curve constructed from the anisotropy of antibody stocks can be used for determining the DOL of the bound fraction. The fluorescence intensity of the cell-bound antibody fractions and of the antibody stocks exhibited distinctly different dependence on the DOL. The behavior of the two dyes was systematically different in this respect. Fitting of the model to these data revealed that labeling with each dye affects quantum yield and antibody affinity differentially. These measurements also implied that fluorophores in multiply labeled antibodies exhibit self-quenching and lead to decreased antibody affinity, conclusions directly confirmed by steady-state intensity measurements and competitive binding assays. Although the fluorescence lifetime of antibodies labeled with multiple fluorophores decreased, the magnitude of this change was not sufficient to account for self-quenching indicating that both dynamic and static quenching processes occur involving H-aggregate formation. Our results reveal multiple effects of fluorophore conjugation, which must not be overlooked in quantitative cell biological measurements.

Introduction

Although bioorthogonal labeling and coupling to fluorescent proteins are widely used for visualizing biological molecules of interest, fluorescent monoclonal antibodies remain the mainstay of labeling approaches (1, 2). Despite their extensive usage, relatively little is known about the quantitative effects of labeling on the properties of antibodies and fluorophores. In general, conjugation of fluorophores to antibodies can be carried out via amino, thiol, and carbohydrate groups (3, 4). Coupling of dyes to ε-amino groups of lysines is by far the most versatile approach in such reactions. Although the labeled antibody is characterized by the degree of labeling (DOL, labeling ratio, the mean number of fluorophores per antibody), the antibody stock solution contains a number of different species with a range of different DOLs due to the availability of many lysine residues and the partially stochastic nature of the labeling reaction (5). Although it has not been rigorously proven theoretically or tested experimentally, the number of fluorophores per antibody is assumed to follow a Poisson distribution (6, 7). Knowing the DOL is necessary for calculations in which the number of bound antibodies is involved, e.g., Förster resonance energy transfer (FRET) and the quantitation of the number of epitopes (8, 9). Although the DOL of the bound antibodies should be used in these equations, the DOL of the antibody stock is used instead due to the unavailability of methods for determining the DOL of the bound fraction. This simplification is based on the assumption that the distribution of labeling ratios in the stock is identical to that in the bound fraction. However, anecdotal and indirect evidence suggests that conjugation of multiple fluorophores to monoclonal antibodies deteriorates the affinity of antibodies (6, 10, 11). Unfortunately, none of these investigations has directly measured the properties of the bound fraction. Another confounding factor is the effect of conjugation of multiple fluorophores to an antibody on the fluorescence quantum yield. This effect, originating from the interaction between neighboring dyes and between dyes and the antibody, ranges from self-quenching, also known as concentration quenching (12, 13, 14, 15), to enhanced fluorescence due to excimer formation or metal-induced effects (14, 16).

In the present study we systematically investigated the effect of labeling with AlexaFluor546 and AlexaFluor647 dyes on the affinity of the antibody and on the photophysical properties of the dyes. After confirming self-quenching and decreased affinity of multiply labeled antibodies we directly estimated the DOL of the bound fraction of antibodies using fluorescence anisotropy measurements and single molecule imaging. We also developed a theoretical framework accounting for the different behavior of AlexaFluor546 and AlexaFluor647 dyes. Fluorescence lifetime measurements showed that self-quenching is the result of mixed dynamic and static quenching processes. Our results emphasize that care must be exercised when interpreting the cell-bound intensity of fluorescently labeled antibodies in quantitative biophysical measurements.

Materials and Methods

Cells

The A431 human epithelial carcinoma cell line overexpressing ErbB1 and the SKBR-3 human breast cancer cell line overexpressing ErbB2 were obtained from American Type Culture Collection (Rockville, MD) and were grown according to their specifications. For microscopic experiments cells were grown in eight-well chambers (Ibidi, Martinsried, Germany) and for flow cytometry they were harvested by trypsinization. The Epstein-Barr virus-transformed human B lymphoblastoid cell line, JY, was grown in RPMI 1640 medium containing 10% heat-inactivated fetal calf serum, 2 mM L-glutamine and antibiotics.

Antibodies

Mouse hybridomas producing the W6/32 (IgG_2a(κ)) monoclonal antibody specific for the heavy chain of MHC-I, L368 (IgG₁(κ)) binding β-2-microglobulin, and L243 (IgG_2a(κ)) recognizing MHC-II molecules were kindly provided by F. Brodsky (University of California, San Francisco, San Francisco, CA). ErbB1 and ErbB2 were labeled by Mab528 and trastuzumab, respectively. Mab528 (IgG_2a) was purified from the supernatant of the HB-8509 mouse hybridoma cell line (ATCC) by protein A affinity chromatography. Trastuzumab (Herceptin, humanized IgG₁(κ)) was purchased from Roche-Hungary (Budapest, Hungary).

The N-Hydroxysuccinimide esters of AlexaFluor546 and AlexaFluor647 dyes (Thermo Fisher Scientific, Waltham, MA) were conjugated to purified monoclonal antibodies via primary amines according to the manufacturer’s specifications. The dye-to-protein labeling ratio (DOL) varied between 0.5 and 6 and it was separately determined for each labeled aliquot by spectrophotometry. Detailed description of the measurement is provided in Supporting Materials and Methods.

Labeling of cells with antibodies

A431 and SKBR-3 cells were used to label ErbB1 and ErbB2 by Mab528 and trastuzumab, respectively. MHC-I, MHC-II, and β2m molecules were labeled by W6/32, L243, and L368 monoclonal antibodies, respectively, on JY cells. In order to record the equilibrium binding of a fluorophore-conjugated antibody freshly harvested cells were washed twice in ice cold phosphate-buffered saline (PBS; pH 7.4) and 10⁵ cells were labeled with a concentration series of either AlexaFluor546- or AlexaFluor647-tagged antibody in 100 μL PBS supplemented with 1 mg/mL BSA on ice in the dark for 30 min. Unbound antibodies were removed by washing twice in PBS, and the cells were fixed in 1% formaldehyde. To determine the affinity of an unlabeled antibody, cells were washed twice in ice cold PBS and 10⁵ cells were incubated with a concentration series of unlabeled antibody in the presence of a constant concentration of dye-conjugated antibody against the same epitope in 100 μL PBS supplemented with 1 mg/mL BSA on ice in the dark for 30 min. Unbound antibodies were removed by washing twice in PBS, and the cells were fixed in 1% formaldehyde. Fluorescence intensities were measured by flow cytometry. Binding curves and competitive binding curves were fitted to obtain the K_d of the labeled and unlabeled antibodies, respectively, as described in the Supporting Material.

Flow cytometry

Flow cytometric measurements were carried out with a FACS Aria III flow cytometer (Becton Dickinson, Franklin Lakes, NY). AlexaFluor546 was excited by a 561-nm laser beam and its fluorescence emission was detected at 595 ± 25 nm, while AlexaFluor647 was excited by a 633-nm laser line and its fluorescence was recorded above 635 nm. The mean fluorescence intensity of cells was analyzed by a custom-written software tool, ReFlex (17), after gating on the live cell population in the forward angle light scatter vs. right angle light scatter dot plots. The mean intensities of labeled samples were background-corrected before further analysis.

Fluorometry, measurement of fluorescence anisotropy

A Fluorolog-3 spectrofluorimeter (Horiba Jobin Yvon, Edison, NJ) was used to measure fluorescence intensity and anisotropy. AlexaFluor546 was excited at 550 nm and its fluorescence was detected at 590 nm, while AlexaFluor647 was excited at 650 nm and its emission was recorded at 675 nm. The excitation and emission slits were adjusted to 10 nm. Antibody stock solutions were diluted to a concentration of 20 nM in order to measure their intensity and anisotropy. The fluorescence anisotropy (r) was measured in the L-format according to the following formula (18):

$$r=\frac{I_{\text{vv}}-G{I}_{\text{vh}}}{I_{\text{vv}}+2G{I}_{\text{vh}}}$$ (1)

where I_vv and I_vh are the vertical and horizontal components, respectively, of the fluorescence excited by vertically polarized light, and G is a correction factor characterizing the different sensitivity of the detection system for vertically and horizontally polarized light:

$$G=\frac{I_{\text{hv}}}{I_{\text{hh}}}$$ (2)

where I_hv and I_hh are the vertical and horizontal components, respectively, of the fluorescence excited by horizontally polarized light. The DOL-dependence of the fluorescence intensity of antibody stocks and of the bound fraction was fitted according to Eqs. 9 and 10 using the global search algorithm in the software MATLAB (The MathWorks, Natick, MA).

Isolation of the cell-bound fraction of antibodies by immunoprecipitation

Five million cells were labeled by AlexaFluor546- or AlexaFluor647-tagged IgGs followed by washing twice in PBS to remove unbound antibodies. Cells were lysed in lysis buffer (20 mM Tris, 0.1% NP-40, 137 mM NaCl, 10% glycerol, 2 mM EDTA-Na and protease inhibitor, pH 8) on ice for 10 min, centrifuged with 600 × g for 5 min and the supernatant was immunoprecipitated with protein G at 4°C for 1 h. The samples were washed three-times with lysis buffer and the protein G-bound antibody was removed from the beads by 100 mM glycin-HCl (pH 3). The eluted antibodies were recovered in the supernatant after centrifugation followed by neutralization by phosphate buffer (pH 7.4). As a control, antibody stock solutions diluted to a concentration of 100 nM were immunoprecipitated and processed in the same way. The fluorescence anisotropy of the immunoprecipitated samples was measured along with the nonimmunoprecipitated stock samples by fluorometry.

Fluorescence lifetime measurements

Fluorescence lifetime measurements were carried out with an inverted IX81 fluorescence microscope (Olympus, Melville, NY) equipped with a Lambert Instruments LIFA fluorescence lifetime imaging module with four modulated LEDs in the 405–640 nm range. AlexaFluor546 was excited with the 527-nm LED using a 510–552 BP filter, and its emission was separated from the excitation light with a 570-nm dichroic mirror and it was measured above 590 nm. AlexaFluor647 was excited with the 639-nm LED through a ZET642/20 band-pass filter, and its fluorescence was recorded using a ZT647rdc-UF2 dichroic mirror, an ET665LP filter and an ET700/75m band-pass filter. The fluorescence lifetimes of 20 μg/mL (∼133 nM) antibody stock solutions with different degrees of labeling were determined in the frequency domain (19). Apparent fluorescence lifetimes were determined from the phase shift and the modulation of the emission signal according to the following equations:

$$\begin{array}{c}{\tau }_{\varphi }=\frac{\tan \varphi }{\omega }\\ {\tau }_m=\frac{\sqrt{1-m^2}}{m\omega }\end{array}$$ (3)

where τ_ϕ and τ_m are the apparent phase and modulation lifetimes, respectively; ω is the modulation frequency; and m and ϕ are the modulation and phase shift values, respectively, of the emission signal. Solutions of unconjugated dyes were used for calibration and the lifetimes of AlexaFluor546 and AlexaFluor647 were adjusted to 4.1 and 1 ns, respectively (20).

Single molecule fluorescence measurements

In order to measure single molecule fluorescence of cell-bound antibodies SKBR-3 cells, grown in eight-well chambers, were labeled by 10 μg/mL AlexaFluor546- or AlexaFluor647-tagged trastuzumab in the presence of a 500-fold or 1000-fold molar excess of unlabeled trastuzumab on ice for 30 min. Unbound antibodies were removed by washing twice in PBS followed by fixation in 1% formaldehyde. To analyze antibody stock solutions at the single-molecule level the same kind of antibodies were immobilized on the surface of epoxy-functionalized coverslips (Nexterion “E,” Schott, Jena, Germany) at a concentration of 0.1 and 0.05 μg/mL. Layers adjacent to the coverslip were imaged in photon counting mode using an LSM880 confocal microscope (Carl Zeiss, Oberkochen, Germany). AlexaFluor546 and AlexaFluor647 were excited by a 543- and a 633-nm laser beam, respectively, and their emission was measured between 575–680 and 638–755 nm, respectively. Images were analyzed in MATLAB. They were smoothed with a Gaussian kernel followed by identification of local maxima using a combination of median filtering, gray-scale opening and extended-maxima transform. A circularly symmetric, bivariate normal distribution was fitted to the intensity profile, I(x,y), around each local maximum:

$$I\left(x,y\right)=bg+\frac{z}{2\pi {\sigma }^2}{e}^{-\left(\frac{{\left(x-{\mu }_x\right)}^2}{2{\sigma }^2}+\frac{{\left(y-{\mu }_y\right)}^2}{2{\sigma }^2}\right)}$$ (4)

where bg is a constant background; z is a scaling factor; σ is the standard deviation; and μ_x and μ_y are the locations of the peak in the x and y directions, respectively. The definite integral of the fitted curve above the background between −∞ and ∞ is equal to z, which was taken to be the photon number corresponding to the peak. If local maxima were identified within a distance corresponding to three-times the standard deviation from each other, multiple bivariate normal distributions were fitted to the peaks simultaneously (21, 22).

Theory

Distribution of antibodies with different degrees of labeling in the bound fraction. The concentration of each species in the antibody solution is assumed to follow a Poisson distribution:

$$f_k=c_{\text{tot}}\frac{DO{L}^k}{k!}{e}^{-\text{DOL}}$$ (5)

where f_k is the concentration of the antibody species with a DOL of k, DOL is the mean degree of labeling, and c_tot is the concentration of the antibody solution. Although the validity of this assumption is questionable (see considerations in the Discussion), it can still be considered to be an approximation whose application does not affect the general conclusions presented in the manuscript. The binding of each individual antibody species to its epitope is described by the following system of equations assuming no ligand depletion, i.e., f_k = f_k,tot:

$$\begin{array}{l}{K}_{d0}f{b}_0=f_0{s}_{\text{unbound}}\\ K_{d1}f{b}_1=f_1{s}_{\text{unbound}}\\ K_{d2}f{b}_2=f_2{s}_{\text{unbound}}\\ \mathrm{...}\\ K_{\text{dn}}f{b}_n=f_n{s}_{\text{unbound}}\\ f{b}_0+f{b}_1+f{b}_2+\mathrm{...}+f{b}_n+s_{\text{unbound}}=s_{\text{tot}}\end{array}$$ (6)

where K_d0, K_d1, K_d2, … correspond to the dissociation constant of the antibody species with a DOL of 0, 1, 2, respectively; s_tot and s_unbound are the total concentration of the binding site and the concentration of the unbound binding site, respectively; f₀, f₁, f₂, … stand for the concentration of the unlabeled antibody, and the concentration of the antibody species with a DOL of 1 and 2, respectively; and fb₀, fb₁, and fb₂ are the concentrations of the receptor-bound antibody species with a DOL of 0, 1, and 2, respectively. The equation set above can be converted to matrix form:

$$\left[\begin{array}{cccccc}{K}_{d0}& 0& 0& \mathrm{...}& 0& -f_0\\ 0& K_{d1}& 0& \mathrm{...}& 0& -f_1\\ 0& 0& K_{d2}& \mathrm{...}& 0& -f_2\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ 0& 0& 0& \mathrm{...}& K_{\text{dn}}& -f_n\\ 1& 1& 1& \mathrm{...}& 1& 1\end{array}\right]\left[\begin{array}{c}f{b}_0\\ f{b}_1\\ f{b}_2\\ \mathrm{...}\\ f{b}_n\\ s_{\text{unbound}}\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ 0\\ \mathrm{...}\\ 0\\ s_{\text{tot}}\end{array}\right]$$ (7)

leading to the following solution:

$$\left[\begin{array}{c}f{b}_0\\ f{b}_1\\ f{b}_2\\ \mathrm{...}\\ f{b}_n\\ s_{\text{unbound}}\end{array}\right]={\left[\begin{array}{cccccc}{K}_{d0}& 0& 0& \mathrm{...}& 0& -f_0\\ 0& K_{d1}& 0& \mathrm{...}& 0& -f_1\\ 0& 0& K_{d2}& \mathrm{...}& 0& -f_2\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ 0& 0& 0& \mathrm{...}& K_{\text{dn}}& -f_n\\ 1& 1& 1& \mathrm{...}& 1& 1\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ 0\\ \mathrm{...}\\ 0\\ s_{\text{tot}}\end{array}\right].$$ (8)

The total fluorescence intensity of the antibody stock solution is the sum of the fluorescence intensities of each individual species:

$$F_{\text{free}}=\sum _{k=1}^{\text{highest}\text{DOL}}{f}_{k}k{Q}_k$$ (9)

where Q_k is the fluorescence quantum yield of the fluorophores in an antibody with k number of bound fluorophores.

The total fluorescence intensity of the bound antibody fraction can be calculated according to the same principle:

$$F_{\text{bound}}=\sum _{k=1}^{\text{highest}\text{DOL}}f{b}_{k}k{Q}_k.$$ (10)

The mean degree of labeling of the bound fraction is given by the equation below:

$$\overline{DO{L}_{\text{bound}}}=\frac{\sum _{k=0}^{\text{highest}\text{DOL}}f{b}_{k}k}{\sum _{k=0}^{\text{highest}\text{DOL}}f{b}_k}.$$ (11)

Anisotropy of a population of antibodies characterized by a certain mean DOL. The anisotropy of a mixture of different antibodies is given by the intensity-weighted average of the anisotropies of different species:

$$r=\frac{\sum _i{\varphi }_i{r}_i}{\sum _i{\varphi }_i}$$ (12)

where r_i is the anisotropy of individual species, and ϕ_i is their fluorescence intensity. The above equation takes the following form for a stock solution of an antibody:

$$r_{\text{free}}=\frac{\sum _{k=1}^{\text{highest}\text{DOL}}{f}_{k}k{Q}_k{r}_k}{\sum _{k=1}^{\text{highest}\text{DOL}}{f}_{k}k{Q}_k}$$ (13)

where Q_k is the fluorescence quantum yield of dyes present in an antibody with a DOL of k. The anisotropy of the bound fraction is given by the equation below:

$$r_{\mathrm{bound}}=\frac{\sum _{k=1}^{\text{highest}\text{DOL}}f{b}_{k}k{Q}_k{r}_k}{\sum _{k=1}^{\text{highest}\text{DOL}}f{b}_{k}k{Q}_k}.$$ (14)

The relative fraction of antibodies with different degrees of labeling present in the free (f_k) and bound (fb_k) fraction was derived in the previous section. However, the anisotropy of an individual species characterized by a certain degree of labeling is difficult to determine. By increasing the degree of labeling, i.e., the number of fluorophores in a cluster undergoing homo-FRET, the anisotropy of the cluster changes due to the following reasons:

• 1)The anisotropy of the cluster of k fluorophores (r_k) decreases with increasing cluster size since the fractional intensity of the initially excited fluorophore fluorescing with high anisotropy decreases at the expense of fluorophores excited by homo-FRET whose anisotropy is much lower. This effect is taken into consideration by equation 18 in the paper of Runnels and Scarlata (23). Assuming that the anisotropy of fluorophores excited by homo-FRET is zero, this equation takes the following form:

$$r_k=r_1\frac{1+{\left(\frac{R_0}{R}\right)}^6}{1+k{\left(\frac{R_0}{R}\right)}^6}=r_1\frac{1+\tau E}{1+n\tau E}$$ (15)

where r₁ is the anisotropy of the fluorophore in the absence of FRET, τ is the fluorescence lifetime of the fluorophore in the absence of FRET, R is the distance between fluorophores, E is the homo-FRET efficiency, and R₀ is the Förster distance corresponding to the dye undergoing homo-FRET. Using the Perrin equation r₁ can be expressed as a function of r₀, the limiting anisotropy, allowing the use of the latter for calculating the anisotropy of the cluster:

$$r_1=r_0\frac{\theta }{\theta +\tau }\Rightarrow r_k=r_0\frac{\theta }{\theta +\tau }\frac{1+{\left(\frac{R_0}{R}\right)}^6}{1+k{\left(\frac{R_0}{R}\right)}^6}=r_0\frac{\theta }{\theta +\tau }\frac{1+\tau E}{1+k\tau E}$$ (16)

where θ is the rotational correlation time.

• 2)Although the lifetime of the cluster does not change as a result of homo-FRET, the initially excited molecule is quenched leading to a shortened lifetime. According to the Perrin equation this phenomenon leads to an increased anisotropy of the initially excited molecule. Because the anisotropy of the initially excited molecule dominates the anisotropy of the cluster, this change will increase the anisotropy of the cluster as a function of the number of fluorophores. Effects 1 and 2 are taken into consideration in Eq. 25 in the article of Runnels and Scarlata (23) which takes the following form assuming that only the anisotropy of the initially excited fluorophore is different from zero:

$$r_k=\frac{r_0}{1+\frac{{\tau }_1}{\tau }\left(\frac{r_0}{r_1}-1\right)}\frac{1+{\left(\frac{R_0}{R}\right)}^6}{1+k{\left(\frac{R_0}{R}\right)}^6}=\frac{{\left(1+{\left(\frac{R_0}{R}\right)}^6\right)}^2{r}_0{r}_1}{\left(1+k{\left(\frac{R_0}{R}\right)}^6\right)\left(r_0+r_1{\left(\frac{R_0}{R}\right)}^6\right)}=\frac{r_0\theta }{\theta +\tau \left(1-E\right)}\frac{1+\tau E}{1+k\tau E},$$ (17)

where τ₁ is the lifetime of the initially excited fluorophore shortened due to homo-FRET.

• 3)Fluorophores in close proximity often quench each other by mechanisms other than homo-FRET which is manifested in a lower than expected increase or explicit decrease in the fluorescence of antibodies as a function of their degree of labeling. If this quenching is dynamic, it shortens the lifetime of the fluorophores increasing the anisotropy as a function of the number of fluorophores in the cluster. Although this effect has not been explicitly considered in the previous paragraphs, it can be taken into account by introducing a DOL-dependent r₁ in Eq. 17 which can be calculated according to the Perrin equation.

Results

Determination of the effect of fluorescence labeling on the affinity of antibodies

To determine the effect of labeling with two different fluorophores, AlexaFluor546 and AlexaFluor647, on the binding affinity of five different IgGs (trastuzumab, Mab528, W6/32, L368, and L243), we selected antibodies with a relatively high DOL and analyzed their saturation binding to cells using flow cytometry. Competitive binding experiments were used to reveal the affinity of unlabeled antibodies. Representative measurement data and their fitting revealing the dissociation constant of the labeled and unlabeled antibodies are shown in Fig. S2. The affinity of one of the antibodies (Mab528) seemed to be relatively resistant to labeling with the AlexaFluor dyes, whereas the dissociation constant of the other four antibodies substantially increased upon labeling (Table 1). While the data corroborate previous evidence (6, 10, 11) showing that conjugation of fluorescent dyes decreases antibody affinity in most cases, it also reveals that conjugation with AlexaFluor647 affects antibody affinity more significantly than labeling with AlexaFluor546.

Table 1.

Dissociation Constants of Unlabeled and Labeled Antibodies Determined by Flow Cytometry

Antibody	Unlabeled	AlexaFluor546		AlexaFluor647
	Kd (μg/mL)	DOL	Kd (μg/mL)	DOL	Kd (μg/mL)
Trastuzumab	0.8 (0.6–1.1)	3.3	1.1 (0.8–1.5)	3.8	1.8 (1–2.5)
Mab528	0.5 (0.4–0.7)	4.5	0.5 (0.2–0.8)	4.5	0.5 (0.4–0.6)
W6/32	2.1 (1.1–3)	4.7	4.7 (3.3–6.2)	4.4	11.9 (10.2–13.6)
L368	6.6 (5.7–7.5)	4.9	9.2 (7.1–11.1)	3.2	80.8 (32.3–129)
L243	5.4 (4.4–6.3)	3.3	6 (3.7–8.3)	4.5	7 (5.7–8.3)

Cells were labeled with a concentration series of labeled antibodies prepared by twofold serial dilution. The mean fluorescence intensity of cells measured in flow cytometry was determined and it was analyzed to determine the K_d of labeled antibodies as described in the Supporting Material. Cells were incubated in the presence of a single concentration of a labeled antibody corresponding to ∼50–75% saturation together with a twofold concentration series of unlabeled antibodies. The mean fluorescence intensity of these cells determined by flow cytometry was analyzed to provide the K_d of the unlabeled antibodies. The K_d values are displayed alongside their 95% confidence intervals.

The fluorescence intensity of free and bound antibodies depend differently on the degree of labeling

A stock solution of an antibody with a certain mean degree of labeling contains a mixture of antibody species with different number of fluorophores whose distribution is usually assumed to be Poissonian. Given the negative impact of fluorescence labeling on antibody affinity it is expected that the dissociation constant of these species will increase as a function of their DOL within the same stock leading to a lower representation of these low affinity species in the bound fraction. This phenomenon could be measured by comparing how the fluorescence intensity of the antibody stock and that of the bound fraction increases as a function of the DOL. Although the fluorescence of unbound antibodies plotted against the mean DOL of the stock increased less steeply compared to the linear increase expected if no self-quenching had taken place, antibodies differed significantly in this respect (Fig. 1; Fig. S3). We also measured the fluorescence intensity of the bound fraction using flow cytometry after cells had been labeled with the antibody stocks whose intensity was measured previously. Not only did the intensity increase of cell-bound antibodies as a function of the DOL lagged behind the linear increase, it also differed from the curves of the stock solutions in most cases (Fig. 1; Fig. S3). We also noted a systematic difference between the two fluorophores. Whereas the fluorescence of cell-bound, AlexaFluor546-labeled antibodies, normalized to the intensity of the antibody with the lowest DOL, was higher than the normalized intensity of the corresponding stock, the opposite relationship was revealed for AlexaFluor647-conjugated antibodies.

Figure 1.

The fluorescence intensity of free and bound antibodies as a function of the degree of labeling. The fluorescence intensity of 20 nM solutions of antibodies with different DOLs was measured using fluorometry. Cells (SKBR-3 for trastuzumab; JY for L368) were labeled with saturating concentrations of the antibodies followed by flow cytometric measurement of the fluorescence intensity of the cell-bound antibody fraction. The fluorescence intensities of the antibody stock and those of the bound fraction were normalized to the intensity measured for the lowest DOL and the normalized intensities are plotted as a function of the DOL. The error bars represent the SE calculated from three measurements. The measured data were fitted according to Eqs. 9 and 10 assuming the quantum yield and the K_d can be expressed as power functions of the number of fluorophores in an antibody species (Q_k = k^x, K_d,k = K_d,0 (k+1)^y, where Q_k and K_d,k are the quantum yield and dissociation constant, respectively, of the antibody species having k number of fluorophores, and K_d,0 is the K_d of the unlabeled antibody). The dashed lines show the expected intensity assuming linear dependence of intensity on the DOL. To see this figure in color, go online.

The measured data were fitted according to Eqs. 9 and 10 assuming the quantum yield and the K_d can be represented as power laws according to the following equations:

$$Q_k=k^x,K_{d,k}=K_{d,0}{\left(k+1\right)}^y$$ (18)

where Q_k and K_d,k are the quantum yield and dissociation constant, respectively, of the antibody species having k number of fluorophores, K_d,0 is the K_d of the unlabeled antibody. Although we are not aware of any theory implicating a power-law dependence of affinity or quantum yield on the degree of labeling, the flexibility of power laws allows adequate approximation of how affinity and quantum yield decrease in multiply labeled proteins. Without loss of generality it was assumed that the quantum yield of the antibody with one bound fluorophore is one. The fits reproduced the main tendencies in the measured data (Fig. 1; Fig. S3) and the fitted powers revealed that the quantum yield of AlexaFluor546 is more profoundly affected by labeling, while AlexaFluor647 primarily deteriorates antibody affinity (Table 2). Because some of the assumptions in the model are simplistic relative to the real behavior of fluorophore-labeled antibodies (e.g., assumed power law dependence, absence of ligand depletion, Poissonian distribution of antibody species with different single molecule DOL; see Discussion), quantitative results of the model are to be interpreted with caution. Nevertheless, application of the model in the fitting led to meaningful results giving clear information about the underlying processes in agreement with other experimental results (e.g., effect of labeling on antibody affinity according to Table 1). We concluded that the distinct dependence of the fluorescence of the bound and free antibody fractions on the DOL supports our hypothesis that antibody species with different DOLs in the same stock solution have different affinities and that the mean DOL of the bound and unbound fractions must be different.

Table 2.

Exponents Obtained from Fitting the DOL-Dependence of the Fluorescence Intensity of the Bound Fraction and that of the Stock

Antibody	AlexaFluor546		AlexaFluor647
	Exponent of the Quantum Yield Term	Degree of the Kd Term	Exponent of the Quantum Yield Term	Degree of the Kd Term
Trastuzumab	−0.41	2.34	−0.44	5.6
Mab528	−0.6	0.46	−0.27	0.11
W6/32	−0.79	1.21	−0.14	4.4
L368	−0.7	0.76	−0.34	1.67
L243	−0.31	0.8	−0.12	1.39

The DOL-dependent intensities presented in Fig. 1 and Fig. S3 were fitted according to Eqs. 9 and 10. The relative quantum yield of fluorophores in an antibody having k number of dyes (Q_k) was modeled by the equation Q_k = k^x, and the dissociation constant of the antibody with k number of fluorophores (K_d,k) was assumed to change according to the equation K_d,k = K_d,0 (k+1)^y, where K_d,0 is the dissociation constant of the unlabeled antibody shown in Table 1.

Simulation of the fluorescence intensity of free and bound antibodies

Although interpretation of the results presented in the previous section implies that fluorophore-dependent changes in the quantum yield and antibody affinity induced by fluorescence labeling take place, our aim was to provide a quantitative explanation for the different behavior of the two AlexaFluor dyes. Details of the model are presented in the Theory. A stock solution of an antibody is assumed to contain a mixture of antibody species with different single molecule DOLs. These fluorescently-labeled IgG species have distinctly different affinities and quantum yields and they compete for binding to the same epitope. The predicted fluorescence intensity of the stock and the bound fraction were calculated for four different conditions according to Eqs. 9 and 10. The results of two relatively trivial borderline cases are shown in Fig. S4. If antibody affinity is not influenced by fluorescence labeling, the normalized fluorescence intensity of the stock and the bound fraction completely overlap even though the quantum yield decreases as a function of the DOL. If the quantum yield is constant, but the affinity of antibodies decrease at high DOL, the fluorescence of the stock increases linearly, while the normalized fluorescence intensity of the bound fraction levels off. Having shown that the model predicts the expected phenomena in trivial cases we analyzed two complex models in which both antibody affinity and dye quantum yield are affected by labeling. In model 1 deterioration of antibody affinity owed to labeling is more emphatic, while in model 2 the quantum yield of dyes is more sensitive to labeling. Models 1 and 2 reproduced the distinct behaviors of the two AlexaFluor dyes in that the normalized fluorescence intensity of the bound fraction was higher in model 2, while that of the stock solution was higher in model 1 (Fig. 2). If the quantum yield is affected more significantly than antibody affinity by fluorescence labeling, the normalized intensity of the bound fraction is predicted to be higher, which was typically the case for AlexaFluor546. On the other hand, if the affinity of the antibody is more sensitive to fluorescence labeling than the quantum yield of conjugated dyes, the normalized intensity of the stock is higher corresponding to typical curves of AlexaFluor647 (Fig. 1; Fig. S3). Although the DOL of the stock increased up to five, the mean DOL of the bound fraction only reached ∼3–4 allowing us to conclude that the predicted mean degree of labeling of the bound fraction is smaller than that of the stock in both models.

Figure 2.

Model calculation of the fluorescence intensity of antibody stocks and that of the bound fraction of antibodies. The fluorescence quantum yield and the dissociation constant of single antibody molecules were assumed to depend on the single molecule degree of labeling. In model 1 (A, graphs on the left) and model 2 (B, graphs on the right) antibody affinity and dye quantum yield, respectively, are affected more significantly by labeling. The dependence of the quantum yield and the dissociation constant on the single molecule DOL is shown in the bottom. Antibody stock solutions with a certain mean DOL were assumed to contain a Poissonian mixture of antibody species with different single molecule DOLs. The intensity of these antibody stocks and the fluorescence intensity of the cell-bound fraction were calculated as described in the Theory according to Eqs. 9 and 10 (graphs on the top). For calculating the cell-bound curves a total antibody concentration of 20 μg/mL was assumed. So that these graphs are comparable to those measured experimentally (Fig. 1; Fig. S3) the intensities are normalized to those calculated for the lowest DOL. The dashed line shows how the fluorescence intensity would depend on the mean DOL if neither the dissociation constant, nor the quantum yield were influenced by labeling. The mean degree of labeling of the cell-bound fraction is shown in the graphs in the middle. To see this figure in color, go online.

Determining the degree of labeling of the bound antibody fraction using fluorescence anisotropy measurements

Although experimental results and modeling presented in the previous sections pointed at a difference between the mean degree of labeling of the bound and unbound antibody fractions, we tried to find an independent confirmation of these results. Because homo-FRET is a sensitive measure of how many spectroscopically identical fluorophores are present within the Förster radius (15, 23, 24, 25, 26), we performed fluorescence anisotropy measurements. Cells were labeled with fluorescent antibodies with different DOLs followed by lysis and immunoprecipitation to isolate the cell-bound antibody fraction whose fluorescence anisotropy was measured alongside that of the stock solutions. In order to reveal any potential effect of immunoprecipitation the stock solutions were also immunoprecipitated using the same protocol as that applied to the antibody-labeled cells. The fluorescence anisotropy of the stock solutions declined as a function of the DOL in accordance with Eqs. 15, 16, and 17. The anisotropies of the untreated stock solutions did not differ from those of the immunoprecipitated stocks implying that the treatment applied to the cells does not have any significant effect on the determined anisotropies (Fig. 3; Fig. S5). On the other hand, the anisotropy of the cell-bound antibody fraction was typically higher than that of the corresponding stock for both AlexaFluor dyes implying that the mean degree of labeling of cell-bound antibodies is lower. In certain cases (e.g., AlexaFluor647-trastuzumab, AlexaFluor546-L368, AlexaFluor647-L368) the anisotropy of the cell-bound fraction hardly decreased when cells were labeled with antibodies with increasingly higher DOL implying that the antibody species with the lowest single molecule DOL bound to the cells almost exclusively. Mab528 was an exception to this rule since the three anisotropy curves almost perfectly overlapped confirming the lack of significant effect of fluorescence labeling on the affinity of this antibody, as already implied by Fig. S3.

Figure 3.

Anisotropy of antibody stocks and cell-bound antibodies as a function of the degree of labeling. The fluorescence anisotropy of 20 nM stock solutions of antibodies with different DOLs was measured by fluorometry (●) and the mean anisotropies were fitted according to Runnels and Scarlata (Eq. 15). Results of the fitting are shown in the bottom left corner of the graphs (d = R₀/R, and r₁ is the estimated anisotropy for a single fluorophore on the antibody, with the 95% confidence intervals displayed in brackets). Antibody stock solutions (○) and cells labeled with antibodies (▲) were immunoprecipitated with protein G and the anisotropy of the isolated antibodies was measured by fluorometry. Error bars represent the SE (n = 3–5).

Although conjugation with AlexaFluor546 and AlexaFluor647 seems to affect antibody affinity differently according to Fig. 1 and Fig. S3, anisotropy measurements (Fig. 3; Fig. S5) revealed the same tendencies for both dyes. Therefore, we applied the model presented in the previous section extended with the dependence of fluorescence anisotropy on the number of fluorophores undergoing homo-FRET (described in detail in the Theory) to the stock solutions and the bound fraction. Results of the calculations predicted that the bound fraction is characterized with a higher fluorescence anisotropy independent of how antibody affinity is affected by dye conjugation (Fig. S6). We used the anisotropy of antibody stocks as calibration curves and read the mean DOL of the bound fraction from these graphs (crosshairs in Fig. S6). The mean DOL of the bound fraction determined from the anisotropy curves agree remarkably well with the calculations presented in Fig. 2 implying that the anisotropy measurements can be used for determining the mean DOL of the bound fraction. The experimental results and the model calculations allowed us to conclude that the mean degree of labeling of cell-bound antibodies is typically lower than that of the stock.

The effect of antibody labeling on the fluorescence lifetime and spectra of fluorophores

Results presented in the previous sections imply that fluorophores in multiply labeled fluorescent antibodies exhibit reduced brightness. To reveal whether static or dynamic quenching processes are behind the phenomenon we carried out fluorescence lifetime measurements in the frequency domain with dilute solutions of the antibody stock solutions. We determined the apparent phase and modulation lifetimes of AlexaFluor546- and AlexaFluor647-tagged antibodies and normalized them to the lifetime of the antibody with the lowest DOL. The fluorescence intensity of the same antibody stocks, measured separately by fluorometry, was also normalized to the intensity of the antibody with the lowest DOL and plotted alongside the normalized lifetimes as a function of the DOL (Fig. 4; Fig. S7). Although the normalized fluorescence lifetimes decreased with increasing DOL, the extent of this change was typically significantly smaller than the change in the normalized fluorescence intensities implying that the majority of the decreased quantum yield is attributable to static quenching. The L243 antibody was a notable exception to this rule with decreases in lifetime almost as large as in its fluorescence intensity (Fig. S7).

Figure 4.

Fluorescence lifetimes and intensities of antibody stock solutions with different degrees of labeling. The fluorescence lifetimes of antibodies were determined in the frequency domain and were normalized to the lifetime of the antibody with the lowest DOL. The unnormalized lifetimes of the antibody with the lowest DOL are shown in every plot. Fluorescence intensities of the same antibody stock solutions were also determined by fluorometry and the intensity values normalized both by the DOL and by the intensity of the antibody with the lowest DOL are also shown for comparison. Error bars represent the SD (n = 3). The lifetimes of the other two antibodies (trastuzumab, L243) are shown in Fig. S7.

In order to reveal whether non-fluorescent dimers, also known as H-aggregates (27), contribute to quenching, absorption and excitation spectra of fluorophores conjugated to antibodies were recorded. The appearance and DOL-dependent increase in a peak blue-shifted relative to the major absorption band in the absorption spectra and the lack of such a peak in the excitation spectra imply that nonfluorescent aggregates are present in multiply labeled antibodies of both dyes (Fig. 5; Fig. S8). Since the absorption spectra of free, unconjugated dyes recorded at 3 and 10 μM completely overlapped (data not shown), dyes do not aggregate in this concentration range and therefore the spectra of unconjugated dye molecules shown in Fig. 5 and Fig. S8 correspond to monomers. The fact that cyanine dyes are known not to aggregate in the low micromolar range also supports the conclusion above (28). In spite of the monomeric nature of free, unconjugated dyes, a peak located at the short wavelength side of the main peak is present in the spectrum, which is presumed to be related to vibronic transitions (28). The excitation spectra of unconjugated, free AlexaFluor647 differs from that of the antibody-bound dye, while these spectra overlap each other in the case of AlexaFluor546. Cyanine dyes are known to form cis and trans isomers whose spectroscopic characteristics are slightly different with the cis isomer having a lower quantum yield and a blue-shifted absorption peak (29). One could assume that the equilibrium between the cis and trans isomers is shifted or the quantum yields of the isomers change differently when AlexaFluor647 is conjugated to an antibody leading to the observed spectral changes, i.e., alterations in the excitation spectrum already at the lowest DOL values. However, the perfect overlap of the excitation spectra of antibody-bound AlexaFluor647 in antibodies with different DOLs argues for the presence of non-fluorescent aggregates of the dye. In conclusion, the lifetime and spectral data are in accordance with quenching caused by dye aggregation.

Figure 5.

Absorption and excitation spectra of AlexaFluor546 and AlexaFluor647 alone and bound to antibodies. The absorption spectra of antibody-conjugated fluorophores at a concentration of 3 μM were recorded by photometry. Excitation spectra of 20 nM solutions of antibodies were recorded at an emission wavelength of 610 and 690 nm for AlexaFluor546 and AlexaFluor647, respectively. Spectra were normalized to the peak value. The absorption and excitation spectra of unconjugated, free dye molecules were recorded at dye concentrations of 3 μM and 20 nM, respectively. To see this figure in color, go online.

Distribution of the fluorescence intensity of single antibody molecules in the stock solution and in the cell-bound fraction

All the previous experimental and theoretical results imply that the mean DOL of the cell-bound antibody fraction is lower than that of the stock due to the lower affinity and consequent underrepresentation of multiply labeled antibody species in the bound fraction. In order to obtain an explicit confirmation for the aforementioned observation and to confirm that application of the previous, indirect methods led to correct conclusions we carried out single molecule fluorescence measurements with antibody stocks and cell-bound antibodies. Performance of the photon counting detector of the microscope was checked by plotting the variance of single pixels against their mean calculated from a time series recorded of immobilized fluorophores (Fig. S9). The fact that the slopes of lines fitted to the variance-mean plots were approximately one indicates that single photon counts are accurately reported by the detectors. Sufficiently diluted antibody stocks were immobilized on the surface of epoxy-functionalized coverslips to ensure that single diffraction limited fluorescence spots correspond to single antibody molecules. For the same reason cells were also labeled with sufficiently diluted fluorescent antibodies. The fact that diffraction limited spots correspond to single fluorophores is usually proven by the observation of single-step bleaching kinetics. However, we could not apply this approach since multiple fluorophores are present in single antibodies. Instead, two samples with differently diluted fluorescent antibodies were prepared with the coverslip-bound antibody stocks and with the cell-bound antibodies as well. The fact that the intensity distribution of fluorescent spots was identical for the two differently diluted samples implies that the spots indeed correspond to individual antibodies (Fig. 6; Fig. S10). The full width at half-maximum and radial symmetry of the intensity profile also suggested that the spots were diffraction limited. We also recorded images of coverslip- and cell-bound AlexaFluor488-conjugated antibodies using microscope settings for AlexaFluor546 and AlexaFluor647. The signal of AlexaFluor488 was used to find the layer adjacent to the coverslip. Since the fluorescence of AlexaFluor488 spills over negligibly to the AlexaFluor546 and AlexaFluor647 channels, these samples served as negative, unlabeled controls demonstrating that the specific signal of AlexaFluor546- and AlexaFluor647-conjugated antibodies is much stronger than the autofluorescence (Fig. S11).

Figure 6.

Single molecule fluorescence measurements of free and cell-bound antibodies. Cells were labeled with the indicated antibodies mixed with a 500-fold or 1000-fold molar excess of unlabeled antibodies to decrease the surface density of labeled, cell membrane-bound antibodies to such an extent that diffraction limited fluorescence spots correspond to single antibodies. Antibody stock solutions of the same kind of antibodies at two different concentrations (0.1 and 0.05 μg/mL) were immobilized on the surface of epoxy-functionalized coverslips. Both the cell-bound antibodies and those covalently cross linked to the surface of epoxy-coated coverslips were imaged under the same conditions. Images were recorded from a layer adjacent to the coverslip in photon counting mode. The intensity of single, diffraction limited fluorescence spots, shown in Fig. S10, was determined from the integral of 2D Gaussian curves fitted to the intensity distribution. The histograms typically represent data from 1000 to 1500 diffraction limited spots. To see this figure in color, go online.

The intensity distribution of fluorescent spots in the stock and cell-bound fraction were compared for AlexaFluor647-conjugated trastuzumab with a high mean DOL (DOL = 3.8). Such an antibody stock is expected to contain several antibody species with those containing three or four fluorophores being the most abundant assuming antibody species with different DOLs are distributed according to the Poisson distribution. However, the lowest intensity peak was the most abundant in the intensity distribution of the stock, which is in contrast to the expectation based on the Poisson distribution (Fig. 6). We attribute this observation to the inverse relationship between the quantum yield and the DOL leading to a lower than expected intensity of antibody species with multiple fluorophores. The mean intensity of the antibody, calculated from the photon counts of individual spots, with a DOL of 3.8 was only ∼25% higher than that of the antibody with a DOL of 0.9 in accordance with results presented in Fig. 1. When comparing the intensity distribution of stocks and cell-bound antibodies molecular species with a higher single molecule DOL were clearly underrepresented in the bound fraction for the AlexaFluor647-trastuzumab with a high degree of labeling (DOL = 3.8). We did not find any significant difference between the intensity distribution of the bound fraction and the stock for AlexaFluor-647-trastuzumab with a low (DOL = 0.9) labeling ratio (Fig. 6). Actually, the fluorescence intensity distribution of the bound fraction of AlexaFluor647-trastuzumab with a DOL of 3.8 was fairly similar to the intensity distribution of the antibody with a low DOL implying that only antibody species with a low single molecule DOL bind in the case of AlexaFluor647-trastuzumab. All of these findings are in agreement with the conclusions drawn from Fig. 3. Underrepresentation of antibody species with a high single molecule DOL in the bound fraction was also found for AlexaFluor546-tagged trastuzumab as well (DOL = 1.9), although the effect was less pronounced than for AlexaFluor647-trastuzumab with a high DOL in agreement with Fig. 3. All these results agree well with experiments presented in the previous sections (Figs. 1, 3, S3, and S5). In conclusion, the results of single molecule fluorescence measurements confirm that the interpretations of flow cytometric and fluorometric intensity measurements and anisotropy experiments were correct, and antibodies with a lower single molecule DOL preferentially bind their antigen in most cases.

Discussion

Previous reports have already reached the conclusion that conjugation of fluorophores leads to the deterioration of antibody affinity (6, 10, 11). It has also been shown that the fluorescence quantum yield of antibody-bound fluorophores is lower than that of the free fluorophore (12, 13). It has even been reported that only a single dye per antibody fluoresces in a sample of antibodies with a mean DOL larger than one, although it has not been elucidated if only antibodies with one bound fluorophore fluoresce or one fluorophore retains its fluorescence properties in multiply labeled antibodies (30). However, a systematic analysis of several antibodies focused on the DOL of the bound fraction supplemented with a quantitative model and single molecule fluorescence measurements has not been carried out. The major findings of the presented experiments are as follows: 1) the fluorescence quantum yield of antibody-conjugated fluorophores decreases as a result of both dynamic and static quenching, with the latter being the dominant factor, according to fluorescence lifetime measurements; 2) the affinity of fluorescent antibodies decreases as a function of the DOL leading to a lower mean DOL of the bound fraction than that of the stock; and 3) according to model calculations and experimental results the distinct behavior of dyes arises from the differential effect of labeling by multiple dyes on antibody affinity and their own fluorescence quantum efficiency, with antibody affinity and dye quantum yield being affected mainly for AlexaFluor647 and AlexaFluor546 labeling, respectively.

Quenching of fluorescence in multiply labeled fluorescent antibodies is dominated by static quenching effects, although dynamic effects also make a contribution. Because the phase and modulation lifetimes differ, the decay kinetics must be multiexponential or nonexponential explaining why the phase lifetimes are shorter than the modulation lifetimes (19). Although only apparent lifetimes were determined without global analysis of frequency-domain data, these are sufficient for comparing the lifetimes of fluorophores under different conditions (19).

Self-quenching or concentration quenching is caused by the formation of dye aggregates (31, 32, 33) and FRET to these nonfluorescent clusters or dimers at the molecular level (13, 34), i.e., these aggregates behave as energy sinks. Based on the comparison of absorption and excitation spectra, this process takes place in both kinds of AlexaFluor dyes. There are ∼90 lysine residues in a typical IgG, many of which are clustered on the antibody surface providing the opportunity for lysine-conjugated fluorophores to aggregate (35). The presence of both dynamic and static quenching according to lifetime measurements is in accordance with the above molecular interpretation. Nonfluorescent clusters (H-aggregates) are ground-state complexes leading to static quenching which does not reduce the fluorescence lifetime (27). FRET from nonaggregated monomeric, antibody-bound fluorophores to these nonfluorescent dimers contributes to dynamic quenching shortening the fluorescence lifetime. Although the same kind of fluorophores interact in this process, it still cannot be considered to be homo-FRET since the monomeric and aggregated dyes are not spectroscopically identical. As opposed to homo-FRET, this process does reduce the fluorescence lifetime since the nonfluorescent aggregates act as traps or quenchers in the energy migration process removing quanta from the ensemble of molecules undergoing homo-FRET. Besides self-quenching reduction of the quantum yield can also result from the interaction of fluorophores with certain amino acids in the antibody leading to a mixture of dynamic and static quenching caused by photoinduced electron transfer and formation of nonfluorescent, ground-state complexes, respectively (36, 37, 38). These latter mechanisms probably do not play an important role in the quenching of AlexaFluor647 because carbocyanine dyes are known to be resistant to quenching by amino acids (39). Because these nonfluorescent aggregates do not contribute to fluorescence emission and do not take part in the homo-FRET network, the dependence of anisotropy on cluster size is expected to deviate from the predictions of the Runnels-Scarlata theory (23).

Static quenching involves the formation of ground-state complexes often modifying not only the fluorescence, but also the absorption properties of dyes (40). If the magnitude of this effect is large, it invalidates the use of absorption spectroscopy for determining the degree of labeling of fluorescent antibodies (see the Supporting Material). Besides this shortcoming, changes in the absorption characteristics of dyes have several other consequences: 1) the fluorescence intensity of these dyes changes modifying their relative contribution to the total emission in Eqs. 9, 10, 13, and 14. This effect can be accounted for by correcting the fluorescence quantum yields by the changed absorption coefficients. 2) Ground-state complexes with altered absorption coefficients will accept energy by FRET differently due to alterations in the overlap integral and their qualities as energy sinks will be affected. It would be challenging to create a model involving these effects as well, since the fraction of dyes present in such ground-state complexes, their altered quantum yields and absorption coefficients would need to be incorporated into the model. However, the major conclusions of the article, based on comparison of the fluorescence or anisotropy of cell-bound and free antibodies, are not affected by these facts, because these phenomena affect both bound and free antibodies.

The photophysical basis of the original stochastic optical reconstruction microscopy method involves the interaction of a reporter fluorophore (e.g., Cy5) with an activator (e.g., Cy3) (41, 42). Because the rate constant of activator-induced photoconversion of the reporter declines to zero at ∼3 nm, the very existence of such a phenomenon implies that fluorescent antibodies contain dye molecules in direct contact with each other. The observation of non-fluorescent aggregates and consequences thereof are in agreement with the presence of such dye clusters in antibodies.

The decreased affinity of multiply labeled species in an ensemble of fluorescent antibodies and their consequent underrepresentation in the bound fraction was suggested by three different kinds of experiments: 1) the comparison of the DOL-dependence of the fluorescence intensity of the stock and that of the bound fraction; 2) comparison of the anisotropy of the bound fraction to that of the stock; and 3) direct measurement of the fluorescence intensity distribution of single antibodies in the bound fraction. Prediction of the anisotropy of the bound fraction using model calculations established that the anisotropy vs. DOL curve measured for antibody stocks can be used as a calibration curve for determining the mean DOL of the bound fraction. The decreased affinity may be the consequence of the altered or inhibited internal flexibility of antibodies required for antigen binding (43, 44). Although antibodies and fluorophores show remarkable difference regarding their sensitivity to fluorescence labeling, the mean DOL of the bound fraction is almost always lower than that of the stock, albeit the DOL-dependence of the fluorescence intensity of the stock and of the bound fraction differ from each other. We have also considered determining the DOL of the bound fraction directly in the same way as the DOL of the stock is determined, but the absorption of the dye is too low to be measurable. We have also attempted to measure the DOL of the unbound antibody fraction after labeling cells, but the signal-to-noise ratio was too low.

The fluorescence intensity distribution of single molecules in stock solutions was not always in agreement with our expectations, e.g., the lowest intensity peak contained the largest number of molecules in the case of AlexaFluor647-conjugated trastuzumab with a high DOL. We attribute this phenomenon to self-quenching and the consequent non-linear change in the intensity of antibodies with the DOL. Alternatively, it must also be considered that the distribution of antibodies in a stock may not follow a Poisson distribution, which may have also led to the aforementioned phenomenon. For the Poisson distribution to be valid for fluorophore-labeled antibodies each lysine residue must be characterized by the same probability of being labeled and subsequent labeling steps must be independent of each other. Because none of these conditions is fulfilled in fluorescence labeling of antibodies, the Poisson distribution is only a rough approximation.

In conclusion, we have laid out an experimental approach for characterizing the effect of fluorescence labeling on antibody affinity and dye quantum yield and showed that both of these parameters are affected in a fluorophore- and antibody-dependent fashion. The quantum yield is decreased by the formation of dye aggregates and energy transfer from nonaggregated fluorophores to nonfluorescent dimers. The decreased affinity of multiply labeled antibody species in a stock solution leads to their underrepresentation in the antigen-bound fraction. The presented findings have important repercussions on experiments in which the fluorescence of antigen-bound antibodies is to be quantified. Quantitative, intensity-based or ratiometric FRET measurements involve the determination of a constant, variably designated by α or G (9, 45), characterizing the relative sensitivity of the system for detecting excited acceptor and donor molecules. If the calibration constant is determined using samples labeled with fluorescent antibodies, normalization of fluorescent intensities with the DOL of antibodies is required (8). Because the DOL of antibody stocks is typically used, the calibration factor is misestimated. In superresolution imaging based on stochastic, reversible switching of dyes localization of single fluorophores is achieved by turning fluorophores on in a sparse subset of molecules. Because superresolved fluorescence images are constructed from such single localizations, under- or overcounting of single fluorophores is a significant problem. The situation is even worse if markers (e.g., antibodies) with multiple fluorophores are used for labeling a molecule of interest. Statistical methods have been developed to account for possible sources of over- and undercounting (e.g., reversible switching between the on- and off-states) typically including the degree of labeling of the antibody. If this parameter is determined using antibody stock solutions, the number of localizations will be misestimated (30, 46, 47). Therefore, antibodies with a low DOL are typically preferred in quantitative fluorescence studies.

Author Contributions

Á.S. and T.S.-S. carried out flow cytometric and fluorometric measurements of fluorescence intensity, determined the K_d of antibodies and their anisotropy and measured their absorption and excitation spectra. Á.S. also wrote the initial version of the manuscript. L.U.-N. performed the fluorescence lifetime measurements. I.R. contributed to the flow cytometric and fluorometric measurement of fluorescence intensities. G.V. interpreted the fluorescence lifetime and anisotropy data and reviewed the manuscript. J.S. contributed to creating the models and reviewed the manuscript. P.N. conceived the project, performed the model calculations and data fitting and reviewed the manuscript.

Editor: David Piston.