Correction of Systematic Bias in Single Molecule Photobleaching Measurements

Abstract

Single molecule photobleaching is a powerful technique to measure the number of fluorescent units in subresolution molecular complexes, such as in toxic protein oligomers associated with amyloid diseases. However, photobleaching can occur before the sample is appropriately placed and focused. Such “prebleaching” can introduce a strong systematic bias toward smaller oligomers. Quantitative correction of prebleaching is known to be an ill-posed problem, limiting the utility of the technique. Here, we provide an experimental solution to improve its reliability. We chemically construct multimeric standards to estimate the prebleaching probability, B. We show that B can be used as a constraint to reliably correct the statistics obtained from a known distribution of standard oligomers. Finally, we apply this method to the data obtained from a heterogeneous oligomeric solution of human islet amyloid polypeptide. Our results show that photobleaching can critically skew the estimation of oligomeric distributions, so that low abundance monomers display a much higher apparent abundance. In summary, any inference from photobleaching experiments with B > 0.1 is likely to be unreliable, but our method can be used to quantitatively correct possible errors.

Significance

Few techniques can compete with single molecule photobleaching (smPB) in determining the stoichiometry of oligomeric complexes, such as of those associated with Alzheimer’s disease. However, one major weakness of the smPB technique is its sensitivity to possible photobleaching before the start of the measurement. In fact, it is known that no reliable inference can be drawn if prebleaching is substantial. We demonstrate a method that uses chemically conjugated complexes of known stoichiometry to correct the inferences. We show that a distribution of islet amyloid polypeptide oligomers, in which the raw data appear to be monomer dominated, are in fact dominated by dimers. smPB-derived inferences reported in the literature, in cases in which prebleaching may have been substantial, may need to be corrected.

Introduction

Single molecule photobleaching (smPB) (1, 2, 3, 4) has emerged as the leading technique to study the number of monomers constituting an oligomer (5,6). Protein oligomerization during cellular function or pathological aggregation (e.g., in Alzheimer’s or Parkinson’s disease) is a major focus of research, and few techniques can match smPB in measuring the stoichiometry of an oligomer in ambient conditions (7, 8, 9). Oligomerization of receptors (10,11) and amyloid proteins (12, 13, 14) are the two areas in which smPB has proved to be an enabling technique. Other techniques such as mass spectrometry can also measure oligomerization (15, 16, 17). A combination of fluorescence correlation spectroscopy (FCS) and Förster resonance energy transfer techniques have also been used to estimate oligomerization, but this is less precise, especially for larger oligomers (18). In contrast, smPB can perform the measurement under physiological conditions and does not perturb weakly associated complexes. Also, it does not have a limitation in the mass of the proteins and can investigate the sample at picomolar concentrations. These features make it a uniquely appropriate technique for biological applications.

In the smPB technique, time-lapse images of individual particles in a low concentration sample are recorded. Individual oligomers are immobilized and well dispersed so that neighboring oligomers are resolved as separate spots in the image, typically recorded using a total internal reflection fluorescence microscope (19, 20, 21, 22). Each of the monomers is labeled with a fluorescent marker molecule. As the fluorescent markers photobleach stochastically, the intensity of the oligomeric spots decrease in steps. Ultimately, all the monomers in an oligomer get photobleached and the signal goes down to the background level. Counting the number of photobleaching steps at each spot directly provides the stoichiometry of the oligomer present at that spot. Statistics comprising all the spots provides the size distribution of the oligomers.

How accurate is this measurement? One major assumption is that there is no photobleaching before the recording starts. Even if the sample has been preserved well before the measurement, focusing the microscope before the actual recording requires that the sample be exposed to light. Unless the fluorescent marker is extremely photostable, it is likely that some photobleaching will occur before the actual measurement starts. This will lead to a systematic underestimation of the number of monomers constituting an oligomer.

As we show here, even a reasonably small probability (e.g., 0.2) of prebleaching can lead to a major misinterpretation of the data. We then examine whether there is a systematic approach to correct this prebleaching. There have been some attempts to correct for the presence of nonfluorescent monomers in an oligomer. These attempts focused on cases in which the oligomers are a single uniform species, so only the number “n” of the n-mer is the parameter that needs to be determined (23). However, determination of the oligomers formed during protein aggregation is more complicated. It contains a distribution of species with different n’s, and this distribution is frequently the major quantity of interest in an experiment. The previous approaches cannot be applied to such cases because there are simply too many unknown parameters. This problem has been shown to be an “ill-posed” problem, and no unique solution exists in which the bleaching probability and the absolute stoichiometry both are unknown (24).

Here, we formulate a method that provides experimental constraints that help us remove the “ill-posed” nature of the problem. As a demonstration, we study a sample consisting of islet amyloid polypeptide (IAPP) oligomers in solution at low concentrations. We analyze the dependence of this experimentally determined distribution on the probability of prebleaching using rules derived from binomial statistics. As an independent measure, we compare the distribution with the average hydrodynamic size of the same oligomeric solution as measured by FCS. Without correction for prebleaching, we find a large discrepancy between the estimates provided by the FCS measurements and the smPB measurements.

We then formulate a procedure to experimentally determine the probability of prebleaching. We chemically synthesize fluorophore n-mers (specifically, dimers and trimers) covalently linked to a small peptide and prepare separate homogeneous solutions of each. Because of prebleaching, the actual measurement gives rise to a distribution of particles consisting of all species from n-mers to monomers. We then derive a photobleaching probability parameter B by comparing this distribution with the known starting distribution. We check the robustness of B by separately deriving it from the dimeric and the trimeric solutions. We then prepare a mixture of the dimers and the trimers at a given ratio and use B to correct the observed distribution to estimate the original starting ratio. The comparison of the corrected ratio and its predetermined value provides a test for the accuracy of this method. Finally, we correct the data obtained from the IAPP oligomers using this B factor. We then compare the FCS-determined sizes of the monomers and the oligomers, with those obtained from the smPB measurements. We obtain a close agreement between the corrected distribution and FCS-measured average. This shows that our correction procedure is reliable.

Materials and Methods

IAPP preparation

Rhodamine (Rh)-labeled IAPP was synthesized using solid phase peptide synthesis (PS3; Protein Technologies, Tucson, AZ) and purified by using high performance liquid chromatography (Shimadzu Prominence, Kyoto, Japan). The protocols have been discussed previously (25). After purification, the peptide was lyophilized. The lyophilized powder was stored at 4°C. A part of the lyophilized powder was dissolved at pH 3.5 water at a concentration of 1 mM, made into aliquots, flash frozen in liquid nitrogen, and preserved at −80°C. Before starting any smPB experiment, an aliquot was taken out and thawed, and an initial stock solution of IAPP was prepared in phosphate buffer saline (PBS) (20 mM Na₂HPO₄ and 150 mM NaCl) at pH 7.5.

Standard bis- and tris-rhodamine-labeled peptide preparation

The short peptide, QKTTKI, was similarly synthesized in an automated solid phase peptide synthesizer (PS3; Protein Technologies) using 9-fluorenylmethoxycarbonyl (Fmoc) chemistry (25). The C-terminal carboxylic acid is amidated as the peptide was synthesized on Rink Amide 4-methylbenzhydrylamine resin. This mimics the natural peptide, which is also C-terminal amidated. Both of the lysine side chains were orthogonally protected with the “Mtt” group in the Fmoc amino acid itself and used for the synthesis (N-α-Fmoc-N-ε-4-methyltrityl-L-lysine). The sequence of the bis-rhodamine-labeled peptide was H₂N-QK(Rh)TTK(Rh)I-CONH₂. The rhodamine (5(6)-carboxytetramethylrhodamine (TAMRA)) moiety was covalently linked to the side-chain amine of the two lysines. On the other hand, for the tris-rhodamine-labeled peptide, a third rhodamine was covalently linked to the free amine at the N-terminal, H(Rh)N-QK(Rh)TTK(Rh)I-CONH₂. All the Fmoc amino acids and reagents were purchased from Merck (Schuchardt, Hohenbrunn, Germany). The peptides were subsequently purified and characterized in the laboratory following a well-established protocol described previously. The purity of these peptides were characterized using matrix-assisted laser desorption/ionization mass spectrometry. Fig. S1 shows the mass spectrum of the bis-peptide, whereas Fig. S2 shows that of the tris-peptide. The data show that the labeling is complete in each case.

smPB sample preparation

The samples were diluted in pH 7.5 PBS to a final concentration of 0.5–2 nM. This was mixed with polyvinyl alcohol solution (PVA) having a concentration of 0.25%. The mixture was then spin coated on the top of a glass coverslip at 3000 rpm at room temperature until a homogeneous film of PVA was formed, and the coverslip became dry (∼30 s). The coverslips were precleaned by using alkali and piranha solutions as described in the previously published article (19). The multimeric standard peptide (bis- and tris-rhodamine labeled) samples were also spin coated using 0.25% PVA at a concentration of 0.5 nM.

smPB experiment

To acquire smPB images, we have constructed a total internal reflection fluorescence microscope using a high numerical aperture objective lens (NA = 1.49, 100×; Nikon, Tokyo, Japan) (19). A 543-nm He-Ne (25-LGR-393-230; Melles Griot, Rochester, NY) laser was used for excitation. A dichroic was used to separate the excitation from emission (565 nm), and the fluorescence was collected using a band-pass filter (605/55 nm, BA577-633, Nikon). The collected fluorescence was then focused into an electron multiplying CCD camera (ANDOR iXON, DV887ECS-UVB). To capture the images, the coverslip was placed on the TIRF microscope and focused on the plane of coverslip containing the fluorescently labeled peptides. The back-aperture power was kept at 1.3 mW, and the frame rate of the camera was kept at 90 ms.

FCS measurements

FCS measurements of subsaturated solution (∼50 nM) of rhodamine-labeled IAPP in PBS (pH 7.5) were performed in a homebuilt instrument as described by us previously (26, 27, 28). Briefly, the experimental setup contains an expanded collimated beam of 543-nm He-Ne laser (Melles Griot) that was focused into the sample solution using 60× water immersion objective (NA = 1.2; Olympus, Center Valley, PA). The same objective was used to collect the fluorescence coming from the focal volume and separated from the excitation laser by using a 552-nm dichroic mirror (Chroma Technology, Bellows Falls, VT) and passed through a band-pass emission filter of 607/75 nm (Semrock, Rochester, NY). The fluorescence was then focused into a 25-μm core diameter optical fiber and sent to a single photon avalanche photodiode (PerkinElmer, Waltham, MA). The fluorescence signals were correlated using a hardware correlator card (ALV5000E; ALV-Laser, Langen, Germany). The autocorrelation curves obtained were fitted using equations containing two free diffusion components and a triplet component as described earlier (27). The hydrodynamic radii of the small IAPP oligomers were determined from the fit. The same oligomer solution was then used in smPB experiments.

Data analysis

To track the particles, we used the TrackMate plugin in Fiji (29). We chose the minimal diameter of the spots as three pixels. The background was suppressed by choosing an appropriate threshold. For example, in the image shown in Fig. 1 A, the threshold intensity was set to 500. This gives us ∼100 spots on the first frame of the image. Because the oligomers were encased in PVA matrix, they were immobile and hence easy to localize in subsequent frames. Spots having overlapping point spread functions were eliminated from the analysis. Spots that were visible for more than 10 frames and had measurable lengths of photobleaching steps were kept for analysis. The background impurity, if any, was studied using the blank coverslip with a thin film of 0.25% PVA. The statistics was then subtracted from the measured IAPP oligomer distribution.

Figure 1.

(A) TIRF image of rhodamine-labeled IAPP on glass coverslip. (B) Shown are time traces observed during bleaching of individual IAPP oligomers and (C) histogram of the IAPP oligomer population. (D) Shown are FCS autocorrelation curves of IAPP oligomers in solution (dark gray) and free rhodamine B in solution (gray) and residuals in respective colors. Scale bar is 5 μm.

Theory

Binomial statistic relates the actual population to the postbleaching population, which can be expressed as follows:

$$N_{n_{fin}}\left(B,n_{max}\right)={\left(1-B\right)}^n\left[\sum _{s=n}^{n_{max}}{C}_{s-n}^s{N}_{s_{ini}}{B}^{s-n}\right],$$ (1)

where N_n denotes the number of “n”-mers, and “s” is a variable (n ≤ s ≤ n_max).

n_max denotes the maximal number of fluorescent labels in a single particle.

The subscripts “ini” and “fin” denote the total number of particles of n-mer that were originally present (“ini”) and finally present according to the model (“fin”), respectively. B is the prebleaching probability.

We estimated the prebleaching probability factor B from chemically synthesized “bis”- and “tris”-labeled peptide. For pure “bis” and “tris” labels, n_max = 2 or 3, respectively, which is a constant, and for any s ≠ n_max, $N_{s_{ini}}$= 0. To probe the relative population of “bis” and “tris” rhodamine labels in a 1:1 mixture, we put n_max = 3 (highest fluorescent stoichiometry present in the mixture) and $N_{s_{ini}}$= 0 if s ≠ (2 or 3). To correct the population of IAPP oligomers, we used n_max = 8 (highest observed stoichiometry of IAPP in the experiment).

$${{\rm X}}^2=\sum _{n=1}^{n_{max}}{\left[N_{n_{fin}}-N_{n_{obs}}\right]}^2$$ (2)

$${{\rm X}}_R^2=\sum _{n=1}^{n_{max}}\frac{{\left[N_{n_{fin}}-N_{n_{obs}}\right]}^2}{N_{n_{fin}}}$$ (3)

$N_{n_{obs}}$ denotes the number of particles of n-mer that are observed from the experiments.

Eqs. 2 and 3 denote Chi square (X²) and reduced Chi square $\left({{\rm X}}_R^2\right)$, respectively. Chi square (X²) shown in Eq. 2 is used for dimers/trimers and their 1:1 mixtures, and reduced Chi square $\left({{\rm X}}_R^2\right)$ shown in Eq. 3 is used for the IAPP oligomers.

Results and Discussion

Measuring IAPP oligomer distribution in solution

A sample of rhodamine-labeled IAPP at ∼1 nM concentration is prepared and subjected to smPB measurements using a total internal reflection fluorescence microscope, as described in the Materials and Methods. Fig. 1 A shows a representative image. We see that at this concentration, the observed spots are well separated as we only observe ∼0.1 molecules per μm² area. The resolution is somewhat larger than the optical resolution limit of this microscope (∼230 nm, λ_em = 570 nm, NA = 1.49). This is because the pixel size is 156 nm, and so the Nyquist limit dictated resolution is ∼310 nm. Hence, the probability of observing two unresolved spots, which can introduce artifacts in our analysis, is small. The frame rate of the camera is 90 ms, and data were obtained typically for 2 min within which the area under observation is nearly completely photobleached.

After selecting the spots above the threshold limit, intensity versus time trace of each individual spot is obtained, as shown in Fig. 1 B. The traces are then manually analyzed for identifying the photobleaching steps. We typically obtain a minimal step size of ∼100 intensity units above the baseline, which is >5× the SD of the baseline. Each spot is assigned an oligomer number, corresponding to the number of photobleaching steps observed. A histogram of the different oligomer sizes present in the solution is shown in Fig. 1 C. This represents an accumulation of five independent experiments with a total of 1282 oligomers. We observe that the monomers dominate the distribution followed by dimers (71% of the monomers). The trimers and tetramers are ∼30 and ∼10% of the population of the monomers, respectively. The rest of the oligomers are ∼4% of the monomer population. The average number of monomers in an oligomer is 1.85.

We obtain an independent measure of the average size of the oligomers by performing an FCS measurement on the solution (Fig. 1 D). Fig. 1 D shows the autocorrelation trace of IAPP oligomers (dark gray) and of rhodamine B, which is used as standard (gray). FCS gives an estimate of 1.69 ± 0.04 nm for the hydrodynamic radius of IAPP oligomers. This value cannot be directly translated into a number of monomers because the hydrodynamic radius depends on the shape of the particle. However, assuming a spherical particle, it predicts 2.89 ± 0.28 mer to be the average size of the oligomer (assuming that rhodamine B has a hydrodynamic radius of 0.57 nm (30,31)). Therefore, the FCS-measured value is considerably higher than the smPB-measured value.

Photobleaching data from a chemically synthesized homogeneous dimeric sample

We hypothesize that this deviation is the result of prebleaching, which would tend to lower the size estimate obtained from smPB. The extent of prebleaching can be measured if we study a sample containing a homogeneous solution of n-mers with a fixed and predetermined value of n, where n is ≥2 (because a photobleached monomer is not an observable species). We prepared a bis-rhodamine-labeled peptide QKTTKI using solid phase synthesis, with rhodamine labels on both the lysine residues. The mass spectrum shows (Fig. S1) that the sample is pure, and it contains negligible quantities of singly labeled peptide. The peptide sequence was chosen to be short and hydrophilic so that the probability of noncovalent association remains low. Moreover, the purified and lyophilized fraction of bis-rhodamine-labeled peptide was initially dissolved in 10% dimethylsulfoxide. This was then diluted to a final concentration of 0.5 nM in water and PVA, the final solution containing 0.01% dimethylsulfoxide and 0.25% PVA. This mixture was then spin coated on a precleaned glass coverslip, in which the PVA polymerizes into a solid substrate, and the molecules are well separated and do not exhibit diffusive movements when they are subjected to TIRF microscopy. Fig. 2 A shows a representative image. Fig. 2 B shows an example of a fluorescence time trace at an individual spot, and the individual photobleaching steps of bis-rhodamine peptide can be observed clearly. In the absence of any prebleaching, all molecules should show two distinct bleaching steps. However, the data show a significant number of single-step events. There are also some triple-step events, which possibly arise either from two molecules accidentally coming closer than the optical resolution limit of the microscope or from a small amount of association between the molecules. However, this number is only 6% of the total population and has been ignored in the subsequent calculations. Fig. 2 C shows the histogram of the experimentally observed population of bis-rhodamine peptide, obtained from 1493 individual particles observed in three separate measurements. The prebleaching probability factor (B) is obtained from Eq. 1 by minimizing with Eq. 2 (given in the Materials and Methods) and setting n_max = 2 and $N_{s_{ini}}=0$ (for any s ≠ 2). The value obtained for B is 0.38 ± 0.01.

Figure 2.

(A) TIRF image of a bis-rhodamine-labeled peptide on glass coverslip, and (B) time traces of the most populated species found after prebleaching measurement. (C) Histogram of the prebleaching measurement of bis-rhodamine-labeled peptide is shown. Scale bar is 5 μm.

Prebleaching measurements from a trimeric sample

The B value as determined above can be useful for correcting an unknown distribution of n-mers, as it should be independent of n. We verify this by measuring the prebleaching of a separately synthesized tris-rhodamine-labeled peptide. The peptide synthesized was the same, but now the N-terminal is also linked to a rhodamine dye. The mass spectrum of this sample (Fig. S2) shows that the population of the bis- or monolabeled sample is negligible in this sample. The photobleaching experiment was carried out as before. Fig. 3 A shows a representative image, and Fig. 3 B shows representative time traces with one, two, and three separate steps of photobleaching. Fig. 3 C shows the histogram of these photobleaching steps, representing the apparent distribution of the oligomers. We use Eq. 1 and set the constraint n_max = 3 and $N_{s_{ini}}=0$ (for any s ≠ 3) to calculate the B factor from these data. We find the factor to be 0.45 ± 0.04. This is in reasonable agreement with the value obtained from the dimer experiment, showing that our measurement and analysis technique is reasonably robust. Henceforth, we employ an average B value of 0.42 ± 0.02 (average and SE from six independent experiments with bis- and tris-rhodamine-labeled peptide) for oligomers in solution. However, the B value will depend on the excitation intensity, which is not uniform across the field of view. So we estimated the amount of prebleaching of the tris-rhodamine-labeled standard in two different regions of the fields of view with reasonably similar intensities. This results in B values that are not very different, as described in Fig. S3. Hence, in all the experiments, we have tried to record the data from the regions in which the uniformity is reasonably good and then averaged over all such regions.

Figure 3.

(A) TIRF image of tris-rhodamine-labeled peptide on glass coverslip. (B) Time traces of the most populated species found after prebleaching measurement are shown. (C) Histogram of the prebleaching measurement of tris-rhodamine-labeled peptide is shown. Scale bar is 5 μm.

Test of the photobleaching correction method

We then ask whether this estimated B value can reliably correct prebleaching errors. The standard dimeric and trimeric samples used previously give us an opportunity to test this correction method. We prepared an equimolar mixture of bis- and tris-rhodamine-labeled peptide and tested their concentrations by smPB before and after correction. The equimolarity was separately tested by FCS, which can accurately measure the concentration of independently diffusing molecules in a homogeneous solution, irrespective of their brightness. A simple measurement of the fluorescence need not be accurate, even after correcting for the brightness in a 3:2 ratio, because there could be some extent of self-quenching involved. Dilution of the separate dimeric and trimeric solutions were adjusted until they presented the same initial value [G(0)] of the measured autocorrelation (Fig. S4). Because G(0) ∼1/N (where N is the average number of fluorescent molecules in the observation volume), this ensures that the concentrations of the bis- and tris-rhodamine-labeled peptides were equal. The constructed histogram from four such repetitive measurements is shown in Fig. 4 A. By using the B value obtained earlier, we estimated the population of both dimer $\left(N_{2_{ini}}\right)$ and trimer $\left(N_{3_{ini}}\right)$ from Eq. 1, as shown in Fig. 4 B. Here, we set the constraint that the population of all the oligomers, other than N = 2 and N = 3, are equal to zero $\left(n_{max}=3\text{and }{N}_{s_{ini}}=0\text{ if s}\ne \left(2\text{ or }3\right)\right)$. The corrected distribution gives a population ratio of 1.15:1, which is in good agreement with the expected value of 1:1. However, there may still be room for further improvement, because a part of the remaining discrepancy may come from the fact that if there is photobleaching during the FCS measurement (though there was no obvious photobleaching), the oligomers will be slightly heterogeneous, and the G(0) value will not measure a proper concentration. In such cases, the equality of G(0) values may not ensure the equality of concentrations. Using the B values of mean + SE (0.44) and mean − SE (0.39) gives a better representation of the reliability of the method. Fig. 4 C shows that the corrected values are 1:0.85 (mean + SE) and 1:1.5 (mean − SE), respectively. These are still in reasonable agreement with the preset value of 1:1. So we conclude that the prebleaching correction method with B values measured from homogeneous samples provides a reliable estimate of the actual population distribution of oligomers in a heterogeneous mixture. However, the estimation is rather sensitive to the B value, so large errors are possible if the B value cannot be determined reliably.

Figure 4.

(A) Histogram obtained from the measurement of equimolar mixture of bis- and tris-rhodamine-labeled peptide. (B) Shown is the reconstructed population of bis- and tris-rhodamine-labeled peptide from the observed population histogram after prebleaching correction. (C) Shown is the corrected population ratio of bis/tris-rhodamine-labeled peptide as a function of bleaching probability B (mean (gray dash), mean + SE (light gray solid), mean – SE (black dash-dot)).

Prebleaching correction of the heterogeneous IAPP solution

We now apply the method to correct the population distribution obtained from the heterogeneous oligomeric solution of IAPP reported in Fig. 1 C. We note that the dye molecule remains the same (rhodamine), but it is possible that the photobleaching characteristics of the dye may be somewhat different when it is attached to IAPP than when it is attached to the QKTTKI peptide. To test this, we measured the length of the photobleaching steps observed from both the samples. The average length of the last photobleaching step (see Fig. S5) is within 20% of each other, showing that the photobleaching characteristics do not vary much between these two peptides.

The maximal stoichiometry that we have observed from the total IAPP oligomer distribution is eight, and we set all populations with N > 8 as zero while employing Eq. 1 for correction. Fig. 5 A shows the distribution of IAPP oligomers after correction using the average B value of 0.42. This shows that the distribution is dominated by dimers and trimers, unlike the monomer-heavy distribution estimated before correction. We see that the N = 2.89 ± 0.28 mer average value obtained from FCS is in reasonable agreement with the corrected value of 2.67 ± 0.13 mer obtained from the smPB experiments. Fig. 5 B shows the distribution of IAPP oligomers as we vary the bleaching probability B from 0.1 to 0.5. It shows how important the correction is even for a small value of B. Fig. 5 C shows a zoomed part of Fig. 5 B and depicts how the distribution changes for B values in the range mean ± SE (0.42 ± 0.02). The measured distribution appears to be quite robust within the error range of B. We note that the statistics is not very reliable for n ≥ 5, but our estimate should be reliable for tetramers and lower oligomers.

Figure 5.

(A) Distribution of IAPP oligomers after correction. (B) Shown are corrected IAPP oligomer distribution as a function of the prebleaching factor B and (C) distribution of IAPP oligomers for B values in the range mean ± SE.

Conclusions

smPB is a powerful technique to determine the stoichiometry of molecular complexes, but it is sensitive to errors induced by photobleaching before the measurement. Using rules of binomial statistics, we show that even a 20% probability of prebleaching can introduce substantial error in the measurement. Unfortunately, if the prebleaching probability is also not known, the problem does not have a unique solution for an unknown heterogeneous distribution.

Here, we suggest a correction procedure for the data by determining the prebleaching factor from a chemically constructed pure multimeric complex. We construct both a dimer and a trimer and measure their B values separately. We show that the agreement between the two independent samples is reasonably good, and the prebleaching factor for rhodamine-labeled peptide is ∼0.42 or 42%. This is a very large correction factor for a molecule that is known to be reasonably photostable. If a molecule is four times more photostable than rhodamine, which covers all the usually used dye molecules, the prebleaching probability would still be more than 10%. We performed point photobleaching measurements (see Fig. S6) to compare the relative B values of four different dyes: rhodamine (TAMRA), Cy3, Cy5, and Atto647N. It appears that all except Atto647N may require some degree of corrections. This implies that many of the smPB experiments reported so far may need a substantial correction in their interpretation of the data. We also note that the B value is expected to be dependent on the environment and therefore should be measured separately for each type of environment.

We then test the robustness of the correction by using an equimolar mixture (concentrations calibrated by FCS) of the dimers and trimers as a test sample. The equimolar mixture was then subjected to photobleaching, and the obtained distribution was corrected with the previously determined prebleaching factor. The initial measurement showed a large number of monomers. After correction, we obtained a dimer to trimer ratio of 1.15:1. This is in good agreement with the preset value of 1:1. We infer that the prebleaching correction methodology is effective.

We then applied the correction strategy to the experimental data obtained from a solution of IAPP. IAPP oligomers are thought to be the most cytotoxic of the aggregate species, but it is important to know which oligomeric species are present in a solution. We find a distribution that is dominated by monomers. After we apply the correction, it is the dimeric population that appears to be the most common, followed by trimers, monomers, and tetramers, respectively. How acceptable is this result? A qualitative verification of the result is possible using FCS. FCS (Fig. 1 D) predicts a hydrodynamic radius that is ∼1.7 nm. It is difficult to predict the number of oligomers that a protein complex of this size might contain without knowing the shape or the degree of compactness. For a reasonably spherical compact protein, such as GFP (molecular weight 27 kDa), the hydrodynamic radius is 2.3 nm (32). This would imply that a protein complex of 1.7-nm radius would have a molecular weight of ∼11 kDa. This implies that the complex would be a 2.52 mer on average. This assumes that the compactness and shape is similar to GFP and neglects the brightness difference between different particles in the heterogeneous solution of IAPP. However, the observed distribution of IAPP, before correction, gives a value only of 1.85. After correction, the value becomes ∼2.67 ± 0.13, which is in much closer agreement with the value obtained from the FCS measurement.

We note that the degree of photobleaching correction that is required depends on the photostability of the dye. Rhodamine (TAMRA) used here is a frequently used single molecule dye (33,34), and the most bleaching-resistant dyes would at best be a few times better. So the corrections would still be substantial. It may be argued that using fluorescently labeled beads at low powers for focusing may provide a solution to the prebleaching issue. However, in our experience, fluorescent beads cause very high background, even away from the beads, likely because of some leaching of fluorescent dye from the beads. This renders this solution unusable. We also note that our correction measurement is not performed simultaneously in the same field. This can in principle be done if the data are collected with a two-color camera that can find the focus with one dye (excited with one laser that does not excite the primary dye), and then photobleaching is carried out with the actual excitation laser. However, the majority of data in smPB are recorded without such an arrangement. In such cases, even a postexperiment correction of the photobleaching may be better than no correction. For measurements in which determining the ratio of the oligomeric population is critical, it would be prudent to measure the prebleaching factor and make necessary corrections.

Author Contributions

S.M. designed the research. S.D. built the TIRF setup, carried out all the experiments, analyzed the data, and co-wrote the manuscript. A.D. synthesized the “bis” and “tris”-labeled peptide molecules and assisted in the experiment.

Editor: Jochen Mueller.