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# A general method to quantify ligand-driven oligomerization from fluorescence-based images

## Abstract

Here, we introduce fluorescence intensity fluctuation spectrometry for determining the identity, abundance and stability of protein oligomers. This approach was tested on monomers and oligomers of known sizes and was used to uncover the oligomeric states of the epidermal growth factor receptor and the secretin receptor in the presence and absence of their agonist ligands. This method is fast and is scalable for high-throughput screening of drugs targeting protein–protein interactions.

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## Data availability

Fluorescence images and ROI files used to generate the FIF spectrograms in this study have been deposited on the Figshare digital repository and are accessible from https://figshare.com/s/77b90d060901fa8b4cb3

## Code availability

The compiled software used for data analysis described in this work has been deposited on the Figshare digital repository and is accessible from https://figshare.com/s/acfd94b21b1105317f56. The computer code is available from the corresponding author upon request.

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## Acknowledgements

We thank L. Miller (Mayo Clinic, Arizona) for provision of the SecR-mEGFP-expressing cells that were used to develop the current cell lines. We also thank M. McBride and A. Klug for assistance with data analysis. This work was partly funded by the National Science Foundation (grant no. PHY-1626450 awarded to V.R.), the Medical Research Council (UK) (grant no. MR/L023806/1 to G.M.) and the UWM Research Growth Initiative (grant nos. 101X333 to V.R. and 101X340 to I.P.).

## Author information

Authors

### Contributions

M.R.S. prepared samples, performed two-photon microscopy measurements, designed and implemented algorithms, performed data analysis and participated in manuscript writing. G.B. implemented data fitting algorithms, wrote the computer program for data reduction and analysis and participated in manuscript writing. R.J.W. and J.D.P. designed the DNA constructs and cell lines, prepared the samples and performed confocal microscopy measurements. D.B. participated in sample preparation and two-photon microscopy measurements. A.E. performed expression and purification of monomeric and multimeric fluorescent proteins. I.P. designed DNA constructs and supervised work on expression and purification of fusion fluorescent proteins. G.M. designed DNA constructs, supervised the work on development of cell lines and confocal microscopy imaging and participated in manuscript writing. V.R. conceived and designed the study, generated algorithms, performed data analysis, supervised the project and wrote the manuscript with contributions from M.R.S., G.B. and G.M.

### Corresponding author

Correspondence to Valerică Raicu.

## Ethics declarations

### Competing interests

M.R.S., G.B. and V.R. have submitted a provisional patent application covering aspects related to the generation, analysis and applications of one- and two-dimensional brightness spectrograms.

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## Integrated supplementary information

### Supplementary Figure 1 Illustration of the data reduction process in two-dimensional FIF spectrometry using two-photon excitation.

a, Typical fluorescence image (out of 42 images comprising 146 cells) obtained from two-photon excitation of Flp-In™ T-REx™ cells expressing fluorescently labeled plasma membrane targeted mEGFP construct (PM-1-mEGFP), and an overlaid polygon (P131) indicating a region of interest (ROI) which comprises a patch of the basolateral membrane of a cell. b, Software-generated image segmentation of the ROI in (a) using the Moving Square method (see Methods and Supplementary Note 3). c, A fluorescence intensity histogram (green circles) of an image segment selected at random, alongside the Gaussian curve (solid red line) used to fit the experimental histogram by adjusting the mean and width of the Gaussian. The intensity binning was set to 25 intensity counts (in arbitrary units). d-e, Normalized frequency distribution obtained from the (d) PM-1-mEGFP expressing cells (2,803 total segments) was simultaneously fit (solid red line) along with a distribution (e) constructed similarly from measurements of cells expressing dimeric, tandem linked mEGFP constructs (2,832 total segments) using a sum of Gaussian functions in order to find brightness of single protomers of mEGFP, $${\varepsilon }_{eff}^{proto}=61.4$$, when measured using the two-photon optical micro-spectroscope.

### Supplementary Figure 2 Comparison of εeff distributions obtained, using two-photon excitation, from solutions of monomers, dimers, tetramers and octamers of fluorescent proteins.

a, Frequency distribution of εeff for solutions of monomeric EGFP monomers containing an oligomerization-inhibiting mutation (A206K) as well as EGFP without that mutation, which is prone to self-association. The average laser power was 15 mW and the integration time was 100 μs per pixel. Each distribution was fit with a Gaussian function to obtain the mean (μ) and standard deviation (SD) of the distribution. Best-fit parameters for mEGFP (red line) were μ = 70.3 and SD = 7.7, and for EGFP (yellow line) were μ = 102.1 and SD = 8.0. b, Average εeff vs. concentration for solutions containing (i) yellow fluorescent protein monomers (YFP) in the presence of 1 mM Dithiothreitol (DTT) (data labeled as ‘YFP + DTT’), (ii) YFP dimers or duplexes, (YFP)2, treated with 1 mM Dithiothreitol (data labeled as ‘(YFP)2 +DTT’) to remove any disulfide bonds formed between the dimers (see Supplementary Note 5), and (iii) a mixture consisting of (YFP)2 dimers plus (YFP)2 dimers fused to each other end to end (that is, through their termini) via disulfide bonds to form $${({\rm{YFP}})}_{2}ss{({\rm{YFP}})}_{2}$$ tetramers (data labelled as ‘$${({\rm{YFP}})}_{2}\& {({\rm{YFP}})}_{2}ss{({\rm{YFP}})}_{2}$$’). Data points and error bars represent μ ± SD obtained by fitting brightness distributions with single Gaussian functions, similar to (a), and as exemplified in (c). As the concentration of molecules increased, self-association via side-by-side interactions between fluorescent proteins occurred, which led to dimer, tetramer, and octamer formation. From the fitting of each curve with an appropriate theoretical model, the best-fit parameter values have been estimated as follows (see Supplementary Note 6). For ‘YFP + DTT,’ that is, $$YFP+YF{P}^{\mathop{\leftrightarrow }\limits^{{K}_{d}}}\begin{array}{c}YFP\\ YFP\end{array}$$: Kd = 6.5 μM, $${\varepsilon }_{eff}^{proto}=35.3$$; for ‘(YFP)2 + DTT,’ that is, $${({\rm{YFP}})}_{2}+{({\rm{YFP}})}_{2}^{\mathop{\leftrightarrow }\limits^{{K}_{t}}}\begin{array}{c}{({\rm{YFP}})}_{2}\\ {({\rm{YFP}})}_{2}\end{array}$$: Kt = 3.8 μM, $${\varepsilon }_{eff}^{proto}=34.2$$; for ‘$${({\rm{YFP}})}_{2}\& {({\rm{YFP}})}_{2}ss{({\rm{YFP}})}_{2}$$’ the model accounts for two quasi-independent reactions, $${({\rm{YFP}})}_{2}+{({\rm{YFP}})}_{2}^{\mathop{\leftrightarrow }\limits^{{K}_{t}}}\begin{array}{c}{({\rm{YFP}})}_{2}\\ {({\rm{YFP}})}_{2}\end{array}$$ and $${({\rm{YFP}})}_{2}ss{({\rm{YFP}})}_{2}^{\mathop{\leftrightarrow }\limits^{{K}_{o}}}\begin{array}{c}{({\rm{YFP}})}_{2}ss{({\rm{YFP}})}_{2}\\ {({\rm{YFP}})}_{2}ss{({\rm{YFP}})}_{2}\end{array}$$, and gives Kt = 3.4 μM, Ko = 0.4 μM, $${\varepsilon }_{eff}^{proto}=33.9$$, and the fraction of YFP protomers within $${({\rm{YFP}})}_{2}ss{({\rm{YFP}})}_{2}$$ tetramers or octamers, α = 20%. The agreement between the $${\varepsilon }_{eff}^{proto}$$ values determined independently from the three experimental curves as well as between the two Kt values is indeed remarkable, confirming the validity of our measurement method. c, Brightness distributions corresponding to the single points indicated by vertical arrows in (b). The vertical dashed lines indicate εeff values of 1×, 2×, and 4× the brightness of monomeric YFP (that is, $${\varepsilon }_{eff}^{proto}$$), as determined from fitting the binding curves in (b), and which correspond to the brightness values of monomers, dimers, and tetramers, respectively. To assemble the histograms in panels (a) and (c), n≥90 brightness values were determined from as many fluorescence intensity distributions, each distribution consisting of 9,840 intensity measurements. The average and SD for each data point in (b) was determined from n≥90 brightness values used to generate distributions as in (a) or (c).

### Supplementary Figure 3 Two-dimensional-FIF results obtained from single-photon excitation of Flp-In T-REx cells expressing the Tyr251Ala,Arg285Ser mutant of the epidermal growth factor receptor (EGFR) in the absence of ligand (−L) or after 10-min treatment with ligand (+L).

a,d (column 1), Surface plots of the frequency of occurrence of effective brightness (εeff) of each protomer concentration using (a) 22,283 and (d) 19,736 total segments to construct the distribution, extracted from 48 and 36 images, respectively (each consisting of several cells). The data were collected from at least two separate experiments. b,e (column 2), Stacks of cross sections through the surface plots in panels (a) and (d) for different concentration ranges; average concentration for each range (in protomer/μm2) is indicated above each plot. Vertical dashed lines indicate the peak positions for the brightness spectra of monomers, dimers, etc., obtained from analysis of the brightness spectrograms of monomeric and tandem mEGFP (see main text), which were used as standards of brightness in the analysis. c,f (column 3), Relative concentration of protomers in each oligomeric species vs. total protomer concentration, as derived from unmixing of the curves in column 2 into Gaussian components. Each data point and its error bar represent the mean ± standard deviation, respectively, of 1,500 different relative fraction values resulting from bootstrapping and refitting the original set of images as described in the Methods section. The εeff distribution for each concentration range was fitted with a sum of six Gaussians; the peak of each Gaussian was set to a value of $$n{\varepsilon }_{eff}^{proto}$$, where n is an integer denoting the number of protomers in a given oligomer size (For example, 1, 2, 4, etc.), while the standard deviations (SD) were fixed. The, $${\varepsilon }_{eff}^{proto}$$ and SD values were obtained from brightness measurements on cells expressing monomeric or dimeric forms of the fluorescent protein mEGFP (see Fig. 1 and Methods). Only the Gaussian amplitudes (An) were adjusted in the process of data fitting in (b), which gave the fraction of protomers (shown in c) corresponding to each oligomeric species via $${n}_{i}{A}_{i}/\sum _{n}n{A}_{n}$$.

### Supplementary Figure 4 Two-dimensional-FIF results obtained from single-photon excitation of CHO cells expressing wild-type SecR in the absence of ligand (−L) or after 10-min treatment with 100 nm agonist ligand (+L).

a,d (column 1), Frequency of occurrence of effective brightness (εeff) for each protomer concentration using (a) 64,619 and (d) 29,839 total segments to construct the distribution, extracted from 113 and 42 images, respectively (each of which contain several cells). The data were collected from at least two separate experiments. b,e (column 2), Stacks of cross sections through the surface plots in panels (a) and (d); average concentration for each range (in protomer/μm2) is indicated above each plot. Vertical dashed lines indicate peak positions for the brightness spectra of monomers, dimers, etc., obtained from (or predicted from) the simultaneous fitting of the PM-1- and PM-2-mEGFP spectrograms used as standards of brightness (see caption to Fig. 2). c,f (column 3), Relative concentration of protomers within each oligomeric species vs. total concentration of protomers, as derived from unmixing of the curves in column 2 into different Gaussian components. Samples were as follows: wild-type SecR treated with vehicle (−L) (a–c) or secretin (+L) for 10 minutes (d–f). Each data point and its error bar represent the mean ± standard deviation, respectively, of 1,500 different relative fraction values resulting from bootstrapping and refitting the original set of images as described in the Methods section. The εeff distribution for each concentration range was fitted with a sum of six Gaussians; the peak of each Gaussian was set to a value of $$n{\varepsilon }_{eff}^{proto}$$, where n is an integer denoting the number of protomers in a given oligomer size (For example, 1, 2, 4, etc.), while the standard deviations (SD) were fixed. The $${\varepsilon }_{eff}^{proto}$$ and SD values were obtained from brightness measurements on cells expressing monomeric or dimeric forms of the fluorescent protein mEGFP (see Fig. 1 and Methods). Only the Gaussian amplitudes (An) were adjusted in the process of data fitting in (b), which gave the fraction of protomers (shown in c) corresponding to each oligomeric species via $${n}_{i}{A}_{i}/\sum _{n}n{A}_{n}$$.

### Supplementary Figure 5 Two-dimensional-FIF results obtained from two-photon excitation of CHO cells expressing wild-type SecR in the absence of ligand (−L) or treatment with ligand (+L) for non-fixed cells.

a,d (column 1), Surface plots of the frequency of occurrence of εeff for each concentration of protomers using (a) 11,251 and (d) 10,282 total segments to construct the distribution, extracted from 60 images for each row (each image consisting of several cells). The data were collected from at least two separate experiments. b,e (column 2), Stacks of cross sections through the surface plots in panels (a) and (d), that is, frequency of occurrence vs. effective brightness for different concentration ranges; average concentration for each range (in protomer/μm2) is indicated above each plot. Vertical dashed lines indicate the peak positions for the brightness spectra of monomers, dimers, etc., obtained from analysis of the brightness spectrograms of monomeric and tandem EGFP (see main text), which were used as standards of brightness in the analysis. c,f (column 3), Relative concentration of protomers within each oligomeric species vs. total concentration of protomers, as derived from unmixing of the curves in column 2 into different Gaussian components. Measurements were performed on cells for a range of 10–40 minutes after treatment with either the vehicle or secretin. Each data point and its error bar represent the mean ± standard deviation, respectively, of 1,500 different relative fraction values resulting from bootstrapping and refitting the original set of images as described in the methods section. The εeff distribution for each concentration range was fitted with a sum of six Gaussians; the peak of each Gaussian was set to a value of $$n{\varepsilon }_{eff}^{proto}$$, where n. is an integer denoting the number of protomers in a given oligomer size (For example, 1, 2, 4, etc.). The, $${\varepsilon }_{eff}^{proto}$$ and SD values were obtained from brightness measurements on cells expressing monomeric or dimeric forms of the fluorescent protein mEGFP (see Supplementary Fig. 1 and Methods). Only the Gaussian amplitudes (An) were adjusted in the process of data fitting in (b), which gave the fraction of protomers (shown in c) corresponding to each oligomeric species via $${n}_{i}{A}_{i}/\sum _{n}n{A}_{n}$$.

### Supplementary Figure 6 Illustration of agonist-induced concentration of wild-type secretin into small focal regions in the membrane for 30-minute treated cells.

Typical fluorescence images of CHO cells expressing wild-type secretin receptor treated with (a) vehicle for 10 minutes or (b) secretin for 30 minutes. The same images as in Fig. 3 were used, that is, 82 images for both panels, each of which contain several cells. Note the ‘punctated’ appearance of membranes in (b), following long-term (that is, 30 minutes) treatment with agonist, which was caused by accumulation of secretin receptors into and endocytic vesicles. This gave rise to inhomogeneous concentration distributions even within the <500 pixel segments used to generate εeff distributions. Such inhomogeneous distribution caused the effective brightness of each ROI segment to take on a continuum of values, likely leading to the observed smearing of the brightness spectrograms (see Fig. 3h). The upper intensity scale of the displayed images were adjusted to reveal texture.

### Supplementary Figure 7 Comparison of the effect of segment size on visualization and quantification of εeff for the data presented in Supplementary Fig. 4.

a–h, Surface plots of the frequency of occurrence of εeff for each concentration of protomers are shown for CHO cells expressing wild-type secretin receptor. The same dataset, secretin receptor treated with vehicle (−L), is presented in all four plots of column 1 (a,c,e,g). Likewise, in column 2 (b, d, f, h), data obtained from cells expressing secretin receptor and treated with ligand (+L) for 10 minutes is displayed in all four graphs. The difference between the plots in a column is the image segment size used to extract effective brightness and concentration values from the cell images. The same images of cells as in Supplementary Fig. 4 were used, which represented 64,619 (−L) and 29,839 (+L) total segments to construct the distributions, which were extracted from 113 and 42 images, respectively (each of which contain several cells). The typical segment size for each of the four rows of graphs is as follows: a,b - entire cells; c,d −5000 pixel2; e,f −2000 pixels2; and h,i −500 pixel2. The figure illustrates that the size of the segment where intensity distributions are being extracted from affects not only the smoothness of the distribution, but also very dramatically the width of the distribution.

### Supplementary Figure 8 Comparison between two different methods of segmentation for Flp-In T-REx cells expressing fluorescently labeled plasma membrane-targeted mEGFP constructs.

a–d, Software-generated image segmentation of different regions using the Moving Square method (see Supplementary Note 3). e–h: Software-generated image segmentation of the same ROIs selected for a–d using the SLIC method (see Supplementary Note 3). The segmentation methods gave similarly good results for all the images used to generate all the figures in the main body of the papers as well as in the supplementary figures.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–8 and Supplementary Notes 1–6

### Supplementary Protocol

Quantifying membrane protein oligomerization using two-dimensional fluorescence intensity fluctuation spectrometry

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Stoneman, M.R., Biener, G., Ward, R.J. et al. A general method to quantify ligand-driven oligomerization from fluorescence-based images. Nat Methods 16, 493–496 (2019). https://doi.org/10.1038/s41592-019-0408-9

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