The Single-Molecule Centroid Localization Algorithm Improves the Accuracy of Fluorescence Binding Assays

Abstract

Here, we demonstrate that the use of the single-molecule centroid localization algorithm can improve the accuracy of fluorescence binding assays. Two major artifacts in this type of assay, i.e., nonspecific binding events and optically overlapping receptors, can be detected and corrected during analysis. The effectiveness of our method was confirmed by measuring two weak biomolecular interactions, the interaction between the B1 domain of streptococcal protein G and immunoglobulin G and the interaction between double-stranded DNA and the Cas9-RNA complex with limited sequence matches. This analysis routine requires little modification to common experimental protocols, making it readily applicable to existing data and future experiments.

Biomolecules, such as proteins and nucleic acids, interact with each other inside cells during their various functions. It is often informative to determine the kinetic and equilibrium constants of these interactions. One can perform binding assays to determine these constants.¹ When combined with singlemolecule detection capability, binding assays can detect the events of single-biomolecule complex formation and dissocia- tion.^2,3 In a commonly used single-molecule assay format, one biomolecule of interest is immobilized on an imaging surface while its binding partner that is fluorescently labeled is introduced in solution. Figure 1a shows a representative frame from a single-molecule movie obtained from such an experiment (Video S1). Each fluorescent spot, which may represent an individual complex formed by two biomolecules, can be detected by single-molecule spot detection routines, and its fluorescence intensity can be extracted through a Gaussian- weighted summation method. The centermost pixel has the highest weight (1.00) in the total intensity calculation, while each of the surrounding pixels has a lower weight (<1.00). A typical Gaussian kernel is shown in Figure 1b. For the sake of simplicity, we will, in this paper, call the surface-immobilized molecules “receptors” and their binding partners in solution “ligands”. When this analysis is performed for every frame in a single-molecule movie, an intensity—time trajectory can be generated for each receptor (Figure 1c). From these trajectories, one can determine the dwell times of ligand- bound (high fluorescence) and unbound (low fluorescence) states.

Figure 1.

Single-molecule fluorescence binding assays. (a) A representative frame from a single-molecule movie obtained by single-molecule fluorescence binding assays. In this case, the immobilized receptors were immunoglobulin G molecules, and the ligands were B1 domain of streptococcal protein G molecules (labeled with Alexa 594). The ligand concentration used here was 10 nM. (b) A close-up of an individual spot. Its fluorescent intensity can be extracted by using a Gaussian-weighted summation method. When all the 7 X 7 pixel intensities are summed, each pixel has a different weight based on its distance from the centermost pixel. The weight of each pixel follows a Gaussian kernel e^{-a4(pixel distance)2}. The spot disappears when the fluorescently labeled ligand dissociates from the receptor. Each pixel shown in panels a and b is 125 nm. (c) An example intensity—time trajectory generated by analyzing and extracting the intensity from each frame in a single-molecule movie. From the intensity—time trajectory, dwell times of the ligand-bound and unbound states can be calculated. (d and e) Using the single-molecule centroid localization algorithm, one can determine the positions of binding events with molecular scale precision. One binding event usually consists of multiple localization events (black marks, Methods). Localization information reveals nonspecific binding events (localization events outside the green circle in panel d) and closely spaced receptors (localization events in different clusters in panel e). (f) On the basis of localization information, one can adjust the intensity—time trajectory shown in panel c to account for measurement artifacts. Specific binding events (colored peaks) were assigned to different receptors, while nonspecific binding ones (gray peaks) were unassigned.

A common artifact, however, in single-molecule fluorescence binding assays comes from nonspecific binding of ligands to the imaging surface. These nonspecific binding events occur randomly and uniformly on the surface unless passivation defects exist, which preferentially attract ligands. Nonspecific binding events can be partly rejected during analysis by including only those events that co-localize with fluorescently labeled receptors through multicolor labeling and imaging.⁴ However, for conventional wide-field microscopy, the diffraction-limited resolution is much larger than the size of a ligand—receptor complex (lateral resolution of ~260 nm at λ_em = 620 nm and objective NA = 1.2). Consequently, diffraction- limited co-localization analysis cannot reject nonspecific binding events that occur closer to a receptor than the resolution; the analyzed intensity—time trajectory of that receptor is therefore “contaminated” by these nonspecific binding events. In some severe cases, intensity—time trajectories obtained around passivation defects could contain mainly nonspecific binding events. Effective surface passivation can alleviate the issue of nonspecific binding [see the comparison between the PEG and dichlorodimethylsilane- Tween 20 (DT20) surfaces (Figure S1)] and is typically required in single-molecule fluorescence binding assays.⁵

In addition to nonspecific binding, insufficient optical resolution can lead to another artifact; i.e., when multiple receptors are located closer together than the resolution, specific binding events at these closely spaced receptors cannot be distinguished. We will define the “minimal detection area” as an area on the imaging surface that has a radius equal to the resolution. Quantitatively, apparent binding rate constant k_on,_app is given by k_on,app = nk_on + AΨ_on,ns, where n is the number of receptors within a minimal detection area, k_on is the specific binding rate constant of a single receptor, A is the size of a minimal detection area, and Ψ_on,ns is the flux of nonspecific binding events per unit ligand concentration (thus Ψ_on,ns has units of μm⁻² μM⁻¹ s⁻¹). The apparent binding rate constant can be falsely high when n is an integer greater than 1 and when the AΨ_on,ns term is non-negligible as compared to k_on.

One way to resolve these issues is to reduce the minimal detection area (or volume for three-dimensional detection). This was previously achieved by using zero-mode waveguides or plasmonic nanoantennas.^6,7 However, these methods are relatively complicated to implement and therefore are not readily accessible to most laboratories. Point accumulation for imaging in nanoscale topography (PAINT⁸) and its derivative DNA-PAINT³ have been used to resolve spatially close receptors. Intermittency in the fluorescence signal required for localization-based super-resolution imaging is linked directly to the kinetic constants of binding and dissociation in PAINT. PAINT therefore has been repurposed to map binding “hot spots” on DNA origamis and to determine the stoichiometry of biological complexes.^9,10 However, these studies largely focused on DNA-based systems.

Here, we propose to use the single-molecule centroid localization algorithm (also used in PAINT) to determine the positions of binding events with molecular scale precision and to enable accurate kinetic measurements of molecular interactions. The stochastic nature of binding and dissociation ensures image sparsity for super-resolution imaging.⁸ When imaged at a resolution comparable to the size of ligand- receptor complexes, specific binding events at a single receptor appear within a small cluster (full width at half-maximum of ~30 nm), where successive binding and dissociation events happen repeatedly (Figure 1d, inside the circle). Random nonspecific binding events occur in a scattered fashion, mainly outside specific clusters (Figure 1d, outside the circle). Closely spaced receptors can also be resolved (Figure 1e). Single molecule localization information thus allows us to correct the raw intensity-time trajectories to remove most measurement artifacts (Figure 1f). On the basis of this additional level of information from the single-molecule centroid localization algorithm, we have developed a workflow to extract the corrected intensity-time trajectories for single receptors as illustrated in Figure S2.

To test the effectiveness of the proposed method, we measured the kinetic and equilibrium constants of the interaction between the B1 domain of streptococcal protein G (pGB1) and rabbit immunoglobulin G (IgG). Because of its generally high binding affinities for IgG from many species, protein G has been used in a variety of immunoassays for the detection of antibodies. The full-length protein G (pG) is made of three almost identical domains (B1-B3) linked by peptide linkers.¹¹ Previous studies have shown that pG has a picomolar affinity for IgG.¹² However, for truncated pG with only two or one of the three repeat domains, their affinities are reduced by 1 or 4 orders of magnitude, respectively.^13–17 We chose to measure the interaction between IgG and pG with only one repeat domain (pGB1), for it is known to be difficult to measure low-affinity interactions (K_D in the approximately micromolar range) with single-molecule methods.¹⁸

We immobilized IgG on a DT20 imaging surface through a biotin-neutravidin linker and added pGB1 that was stoichio- metrically labeled with Alexa 594 at a single cysteine residue (Methods) in solution (Figure 2a). Long single-molecule movies (30–40 min) were taken so that we could obtain enough binding and dissociation events (12–16 events on average) for each IgG molecule to calculate single-molecule kinetic constants. k_on and k_off were determined from intensity— time trajectories as the reciprocals of the average dwell times of the unbound and bound states, respectively, after removing artifacts based on localization information (Figure 2e and raw trajectories in Figure S3). The left panel of Figure 2b shows the scatter plot of the k_on and k_ofF values with each point representing an individual IgG molecule. The mean k_on, k_off, and K_D values were 0.73 ± 0.34 μM⁻¹ s⁻¹, 0.62 ± 0.29 s⁻¹, and 0.94 ± 0.45 µM, respectively. Previously measured k_on, k_off, and K_D values ranged from 0.14 to 0.29 μM⁻¹ s⁻¹, from 0.027 to 0.76 s⁻¹, and from 0.091 to 5.3 μM, respectively.^14–17 All previous studies used Fc fragments of IgG molecules from various sources and clones, and their measurements were performed in ensemble except for those of ref 13. In general, our results are in the same range as those previously measured. The surface density of IgG molecules was 0.75 μm⁻², as determined by the number of detected clusters per imaging area (Figure 2b, right).

Figure 2.

Binding assays for the pGB1-IgG interaction. (a) Schematics of measuring the pGB1-IgG interaction. (b) Scatter plot of the k_on and k_off values for each measured IgG molecule [N =198 (left)]. The mean and standard deviation of the k_on and k_off values are indicated by the red label and error bars, respectively. A representative density map of localization events shows the positions of detected IgG molecules (right). The surface density of IgG molecules was 0.75 μm^-2. (c) Fluorescence intensity histograms of pGB1-bound states, obtained with (top) and without (bottom) localization information at 0.75 IgG μm^-2. (d) Same as panel b except that the surface density of IgG molecules was increased to 5.3 μm⁻² and N = 272. The color bar in panels b and d indicates the number of localization events at each bin of the density maps (13 nm X 13 nm) (e) A representative intensity-time trajectory of the pGB1-IgG interaction at 5.3 IgG μm^-2. Using the method described for panels e and f of Figure 1 and Figure S2, intensity peaks were assigned to clusters. Intensity peaks colored dark blue belonged to the same IgG molecule. Other intensity peaks (light blue) belonged to either nonspecific binding events or closely spaced IgG molecules.

A histogram of the fluorescence intensity of single complexes (N = 198) showed a single peak when localization information was used in analysis (Figure 2c, top), suggesting that pGB1 and IgG predominantly formed 1:1 complexes at 10 nM pGB1. The wide distribution of intensity is likely due to the nonuniformity in the illumination pattern. In contrast, an additional low- intensity peak showed up in the histogram obtained without localization information (Figure 2c, bottom). This second peak is likely due to binding events occurring slightly away from the receptors where the Gaussian kernel was centered, and those binding events were excluded from analysis when localization information was used. Because these two intensity peaks are largely overlapping, it is practically difficult to separate them through simple intensity thresholding, which emphasizes the necessity of using the single-molecule centroid localization algorithm to distinguish spatially close binding events. To estimate the contribution of the photobleaching rate to the estimated value of k_off, we doubly labeled pGB1 with Alexa 594 and biotin and directly immobilized it through a biotin— neutravidin linker. The photobleaching rate was negligible (0.005 s⁻¹) compared to the k_off value measured above (Figure S4).

We observed a relatively large variation in the measured k_on and k_off values among individual IgG molecules (Figure 2b). Because we collected only a finite number of dwell times for each IgG molecule (on average 12–16), we sought to determine how much variation is due to statistical uncertainty coming from finite sampling. We performed Gillespie simulation of the stochastic process of ligand binding and dissociation, with the experimental trajectory length and average rate constants as simulation parameters. The k_on and k_off values determined from the simulation had the same mean values as the experimental ones but a smaller standard deviation compared to that of the experimental ones (Figure S5), suggesting that additional heterogeneity among surface- immobilized IgG molecules is required to explain the observed variation.

We then increased the surface density of IgG molecules from 0.75 to 5.3 μm⁻² so that a diffraction-limited minimal detection area would likely contain multiple IgG molecules. The kinetic and equilibrium constants measured at the high IgG density agreed well with those measured at the low density [k_on = 0.80 ± 0.42 μM⁻¹ s⁻¹, k_off = 0.60 ± 0.47 s⁻¹, and K_D = 0.83 ± 0.48 μM (Figure 2d,e and raw trajectories in Figure S6)], demonstrating the effectiveness of our method in resolving closely spaced receptors. In comparison, when the same single molecule movies were analyzed without localization information, the measured k_on values increased to 1.1 ± 0.75 and 2.8 ± 1.3 μM⁻¹ s-1 for the cases of low and high IgG densities, respectively, and the measured K_D values decreased to 0.71 ± 0.46 and 0.20 ± 0.22 μM, respectively. The measured k_off values remained similar between two analyses (Figure S7). Using localization information as our “ground truth”, we estimated the contribution of each type of artifact to these falsely high k_on values. At 0.75 IgG μm⁻², 67% of the trajectories analyzed without localization information were “contaminated” by nonspecific binding events (Figure 1d) and 34% contained multiple (on average 2.5) IgG molecules under a diffraction- limited minimal detection area (Figure 1e). At 5.3 IgG μm⁻² 80% of the trajectories were “contaminated” by nonspecific binding events and 97% contained multiple (on average 3.4) IgG molecules. Further analysis of nonspecific binding events on the imaging surface without immobilized IgG molecules yielded a Ψ_0n,_ns value of 0.16 μm⁻² μM⁻¹ s⁻¹ (k_on,ns = AΨ_on,ns ≈ 0.06 μM⁻¹ s⁻¹) and revealed that these events can be either transient or long-lived with the overall k_off,ns value of 0.21 s⁻¹ (Figure S1). Overall, ~10% of all events were due to nonspecific binding when trajectories were analyzed without localization information. In addition, specific and nonspecific binding events had similar dissociation rate constants, partly explaining why k_off was not grossly miscalculated by conventional analysis.

Because the single-molecule centroid localization algorithm requires a certain level of image sparsity, ineffective surface passivation could affect the performance of centroid localization by attracting a large amount of long-lived nonspecifically bound ligands. Therefore, our method requires the use of reasonably well passivated imaging surfaces. For the same reason, the image sparsity condition also limits the surface density of receptors.⁹ With 0.75 IgG μm⁻² on the surface and 10 nM pGB1 in solution, we found the image sparsity condition was satisfied; with 5.3 IgG μm⁻² on the surface, we could observe, in some frames, inaccurate centroid localization due to partially overlapping point spread functions (PSFs) where the surface density of receptors was high (data not shown). Because inaccurate centroid localization could affect the peak calling in our method, these regions were excluded from the analysis (Figure S8). The accuracy of centroid localization in high- density regions can be potentially improved by employing a more advanced centroid localization algorithm that was designed to localize partially overlapping PSFs.^19–21

Next, we tested the versatility of our method by measuring the interaction between double-stranded DNA (dsDNA) and the Cas9-RNA complex. The Cas9-RNA complex consists of the endonuclease Cas9 and a guide RNA (gRNA). Cas9-RNA complex binding requires a protospacer-adjacent motif (PAM) on the target strand of dsDNA, and the k_off of this interaction depends on the length of matched sequences between gRNA and DNA adjacent to PAM. When there is only a short match (<9 bp) adjacent to PAM, Cas9-RNA complex binding is transient.²² We used a DNA that has 4 bp PAM-proximal matches and 16 bp mismatches relative to the gRNA and a catalytically inactive mutant of Cas9.²² The gRNA was biotinylated and immobilized on a PEG imaging surface through a biotin-neutravidin linker, while the DNA labeled with Cy3 was added in solution (Figure 3a). The kinetic and equilibrium constants were determined with the same method described above, and the measured k_on, k_off, and K_D values were 2.3 ± 1.9 μM⁻¹ s⁻¹, 0.82 ± 0.66 s⁻¹, and 0.48 ± 0.34 μM, respectively (Figure 3b,c and raw trajectories in Figure S9), in agreement with those previously measured by single-molecule FRET between a Cy3 (donor)-labeled DNA immobilized on the surface and a Cy5 (acceptor)-labeled Cas9—RNA complex in solution (k_on = 4—8 μM⁻¹ s⁻¹, and k_off = 0.8—4 s⁻¹).²² In comparison, when the same single-molecule movies were analyzed without localization information, the measured k_on, k_off, and K_D values became 2.4 ± 1.5 μM⁻¹ s⁻¹, 0.91 ± 0.71 s⁻¹, and 0.42 ± 0.26 ^M, respectively. We did not observe an improvement using localization information likely because the receptor density was not high, and the PEG surface was effective in preventing the nonspecific binding of DNA

Figure 3.

Binding assays for the interaction between dsDNA and the Cas9-RNA complex. (a) Schematics of measuring the interaction between dsDNA and the Cas9-RNA complex. The PAM motif (yellow) is adjacent to a 4 bp match (red) and then a 16 bp mismatch (black) region to the gRNA. (b) Scatter plot of the k_on and k_off values for each measured Cas9-RNA complex [N = 151 (left)]. The mean and standard deviation of the k_on and k_off values are indicated by the red label and error bars, respectively. A representative density map of localization events shows the positions of detected Cas9-RNA complexes (right). The surface density of Cas9-RNA complexes was 0.80 μm^-2. The color bar in panel b indicates the number of localization events at each bin of the density map (13 nm X 13 nm). (c) A representative intensity—time trajectory of the interaction between dsDNA and the Cas9—RNA complex. Using the method described for panels e and f of Figure 1 and Figure S2, intensity peaks were assigned to clusters. Intensity peaks colored dark blue belonged to the same Cas9—RNA complex. Other intensity peaks (light blue) belonged to either nonspecific binding events or closely spaced Cas9— RNA complexes.

In summary, we demonstrated that the accuracy of fluorescence binding assays can be improved by using the single-molecule centroid localization algorithm. The two major artifacts in this type of assay, i.e., nonspecific binding events and optically overlapping receptors, can be detected and corrected during analysis. For instance, apparent binding rate constant k_on,app of the pGB1-IgG interaction on the DT20 surface is equal to n X 0.73 μM⁻¹ s⁻¹ + A X 0.16 μm⁻² μM⁻¹ s^-1. With localization information, n is equal to 1. Also, because the minimal detection area is reduced after data acquisition through the single-molecule centroid localization algorithm, the AΨ_on,ns term is reduced at least 100 times compared to that of conventional analysis (and this is considering a moderate 10 times higher lateral resolution in the x and y directions). Besides, having high densities of receptors allows us to obtain the same amount of data with relatively small EMCCD regions. Therefore, we can image at a higher time resolution with a higher efficiency. This analysis routine requires little modification to common experimental protocols and could be performed synergistically with existing methods (e.g., multicolor co-localization analysis), making it readily applicable to existing data and future experiments.

Supplementary Material

Supporting Information

Experimental details and supplementary figures (PDF) Movie 1 (AVI)