A Method for Quantifying Molecular Interactions Using Stochastic Modelling and Super-Resolution Microscopy

We introduce the Interaction Factor (IF), a measure for quantifying the interaction of molecular clusters in super-resolution microscopy images. The IF is robust in the sense that it is independent of cluster density, and it only depends on the extent of the pair-wise interaction between different types of molecular clusters in the image. The IF for a single or a collection of images is estimated by first using stochastic modelling where the locations of clusters in the images are repeatedly randomized to estimate the distribution of the overlaps between the clusters in the absence of interaction (IF = 0). Second, an analytical form of the relationship between IF and the overlap (which has the random overlap as its only parameter) is used to estimate the IF for the experimentally observed overlap. The advantage of IF compared to conventional methods to quantify interaction in microscopy images is that it is insensitive to changing cluster density and is an absolute measure of interaction, making the interpretation of experiments easier. We validate the IF method by using both simulated and experimental data and provide an ImageJ plugin for determining the IF of an image.


Supplementary Figure 4
Comparison of the R-G IF with other Measures (a) Plots of the number of overlaps (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster number for R-G IF = 0 (i) and R-G IF = 0.90 (ii). (i) Simulations for R-G IF = 0 show that the number of overlaps increases with increasing red cluster number (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant. (ii) Simulations for R-G IF = 0.90 show that the number of overlaps increases with increasing red cluster number (One-way ANOVA: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster number). (iii-iv) Plots of the number of overlaps (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster size for R-G IF = 0 (iii) and R-G IF = 0.90 (iv). (iii) Simulations for R-G IF = 0 show that the number of overlaps increases with increasing red cluster size (One-way ANOVA: p < 0.0001) while R-G IFs remain constant. (iv) Simulations for R-G IF = 0.90 show that the number of overlaps increases with increasing red cluster size (Oneway ANOVA: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster size).
(b) Plots of the area of overlaps (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster number for R-G IF = 0 (i) and R-G IF = 0.90 (ii). (i) Simulations for R-G IF = 0 show that the area of overlaps increases with increasing red cluster number (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant. (ii) Simulations for R-G IF = 0.90 show that the area of overlaps increases with increasing red cluster number (One-way ANOVA: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster number). (iiiiv) Plots of the area of overlaps (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster size for R-G IF = 0 (iii) and R-G IF = 0.90 (iv). (iii) Simulations for R-G IF = 0 show that the area of overlaps increases with increasing red cluster size (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant. (iv) Simulations for R-G IF = 0.90 show that the area of overlaps increases with increasing red cluster size (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster size).
(c) Plots of the Mander's coefficient 1 for the red overlaps (M1: gray) and calculated R-G IF (red) for simulations generated with increasing red cluster number for IF = 0 (i) and IF = 0.90 (ii). (i) Simulations for R-G IF = 0 show that M1 remains constant with increasing red cluster number (Kruskal-Wallis H test: p = 0.79). (ii) Simulations for R-G IF = 0.90 show that M1 decreases with increasing red cluster number (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster number). (iii-iv) Plots of M1 (gray) and predicted R-G IF (red) for simulations generated with increasing red cluster size for R-G IF = 0 (iii) and R-G IF = 0.90 (iv). (iii) Simulations for R-G IF = 0 show that M1 remains constant with increasing red cluster size (Kruskal-Wallis H test: p = 0.75). (iv) Simulations for R-G IF = 0.90 show that M1 decreases with increasing red cluster size (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster size).
(d) Plots of the Mander's coefficient 2 for the green overlaps (M2: gray) and calculated R-G IF (red) for simulations generated with increasing red cluster number for R-G IF = 0 (i) and R-G IF = 0.90 (ii). (i) Simulations for R-G IF = 0 show that M2 increases with increasing red cluster number (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant. (ii) Simulations for IF = 0.90 show that M2 increases with increasing red cluster number (One-way ANOVA: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster number). (iiiiv) Plots of M2 (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster size for R-G IF = 0 (iii) and R-G IF = 0.90 (iv). (iii) Simulations for R-G IF = 0 show that M2 increases with increasing red cluster size (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant. (iv) Simulations for R-G IF = 0.90 show that M2 increases with increasing red cluster size (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster size).
(e) Plots of the Pearson's coefficients (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster number for R-G IF = 0 (i) and R-G IF = 0.90 (ii). (i) Simulations for R-G IF = 0 show that the Pearson's coefficients remain constant with increasing red cluster number (One-way ANOVA: p = 0.09). (ii) Simulations for R-G IF = 0.90 show that the Pearson's coefficients change with increasing red cluster number (Kruskal-Wallis H test: p = 0.02) while R-G IFs remain constant (means and SD: n = 20 images per cluster number). (iii-iv) Plots of the Pearson's coefficients (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster size for R-G IF = 0 (iii) and R-G IF = 0.90 (iv). (iii) Simulations for R-G IF = 0 show that the Pearson's coefficients increase with increasing red cluster size (One-way ANOVA: p = 0.02) while R-G IFs remain constant. (iv) Simulations for R-G IF = 0.90 show that the Pearson's coefficients increase with increasing red cluster size (One-way ANOVA: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster size).
(f) Plots of the percentage of red overlaps (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster number for R-G IF = 0 (i) and R-G IF = 0.90 (ii). (i) Simulations for R-G IF = 0 show that the percentage of red overlaps remains constant with increasing red cluster number (Kruskal-Wallis H test: p = 0.58). (ii) Simulations for R-G IF = 0.90 show that the percentage of red overlaps decreases with increasing red cluster number (Kruskal-Wallis H test: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster number). (iii-iv) Plots of the percentage of red overlaps (gray) and calculated R-G IF (red) for simulations generated with increasing red cluster size for R-G IF = 0 (iii) and R-G IF = 0.90 (iv). (iii) Simulations for R-G IF = 0 show that the percentage of red overlaps increases with increasing red cluster size (One-way ANOVA: p < 0.0001) while R-G IFs remain constant. (iv) Simulations for R-G IF = 0.90 show that the percentage of red overlaps increases with increasing red cluster size (One-way ANOVA: p < 0.0001) while R-G IFs remain constant (means and SD: n = 20 images per cluster size).

Supplementary Figure 5
Additional measurements for experimental datasets (a) Number and total area covered by pDNA-PKcs and LigIV clusters. (i) The number of pDNA-PKcs clusters was greater in the DNA-damaged compared to control group (****p<0.0001; Student's t-test). (ii) The total area of pDNA-PKcs clusters was greater in the DNA-damaged compared to control group (****p<0.0001; Welch's t-test). (iii) The number of LigIV clusters was greater in the control compared to DNA-damaged group (**p<0.01; Student's t-test). (iv) The total area of LigIV clusters was greater in the DNA-damaged compared to control group (****p<0.0001; Student's t-test). Groups: control (n = 21) and DNA-damaged group (n = 29). Error bars represent 95 CI.
(b) Number and total area covered by pATM and LigIV clusters. (i) The number of pATM clusters in the control group was not significantly different from the DNA-damaged group (n.s. = not significant; p>0.05; Student's t-test) (ii) The total area of pATM clusters was not significantly different in the control compared to DNA-damaged group (n.s. = not significant; p>0.05; Student's t-test). (iii) The number of LigIV clusters was not significantly different in the control compared to DNA-damaged group (n.s. = not significant; p>0.05; Student's t-test). (iv) The total area of LigIV clusters was not significantly different in the control compared to DNA-damaged group (n.s. = not significant; p>0.05; Student's t-test). Groups: control (n = 25) and DNAdamaged group (n = 13). Error bars represent 95 CI.
(c) Number and total area covered by BRCA1 and BRIP1 clusters. (i) The number of BRCA1 clusters was greater in the DNA-damaged compared to control group (****p<0.0001; Student's ttest). The total area covered by BRCA1 clusters was greater in the DNA-damaged compared to control group (****p<0.0001; Student's t-test). The number of BRIP1 clusters was greater in the DNA-damaged compared to control group (***p<0.001; Student's t-test). The total area covered by BRIP1 clusters was greater in the DNA-damaged compared to control group (***p<0.001; Student's t-test). Groups: control (n = 17) and DNA-damaged group (n = 18). Error bars represent 95 CI.
Supplementary Figure 6 Percentage of Overlaps and IF measurements when reference color is changed in experimental datasets (a) LigIV and pDNA-PKcs measurements. (i) Percentage of pDNA-PKcs clusters overlapping with LigIV was greater in the DNA-damaged compared to control group (****p<0.0001; Welch's t-test). (ii) Interaction Factor (IF) between LigIV/pDNA-PKcs in control and DNA-damaged group. The IF between LigIV/pDNA-PKCcs was greater in the DNA-damaged compared to control group (****p<0.0001; Welch's t-test). Groups: control (n = 21) and DNA-damaged group (n = 29). Error bars represent 95 CI.
(c) BRIP1 and BRCA1. (i) Percentage of BRCA1 clusters overlapping with BRIP1 was not significantly different in the DNA-damaged compared to control group (n.s = not significant; p>0.05; Student's t-test). (ii) Interaction Factor (IF) between BRIP1/BRCA1 in control and DNAdamaged group. The IF between BRIP1/BRCA1 was not significantly different in the DNAdamaged compared to control group (n.s. = not significant; p>0.05; Student's t-test). Groups: control (n = 17) and DNA-damaged group (n = 18). Error bars represent 95 CI. Comparison of calculation of R-G IF with and without rotation for clusters with increasing major axis diameter (a) Examples of simulations generated with 100 red clusters and100 green clusters with different major axis diameter. For illustration purposes, the color red is represented as magenta. In generating the simulated images, cluster numbers and size distributions were sampled from experimental image and the major axis diameter was multiplied by 1 (1x), 2 (2X), or 4 (4X).

Introduction
This plugin provides a method for quantifying protein-protein interactions by using stochastic modeling of super-resolution fluorescence microscopy data (RGB images). The result is an unbiased measure of co-localization of protein clusters, independent of cluster density and comparable across images.
Please refer to manuscript (REF) for a detailed description of the Interaction Factor.

Installation
Copy the .jar file into the plugins folder of ImageJ or Fiji. Close and open ImageJ/Fiji. The plugins will be found under Analyze.

Figure 1. Interaction Factor Package
Important Installation Note: the plugin only works with Java8 and ImageJ v1.48 or newer. Download ImageJ bundled with Java8 here

How To Use the Interaction Factor Plugins
For both versions of the plugin, the first step is to start the Fiji or ImageJ application.
Next, choose an image you wish to analyze. This is accomplished by using File/Open menu option or by dragging and dropping a file to the area under the Fiji toolbar. The next step is to choose the plugin which is found under the Analyze pull down menu. There are two versions of the plugin that may be used to analyze an image. The first version, called Interaction Factor, allows you to calculate the Interaction Factor for the image. The second version, called Interaction Factor Simulations, allows you to produce any number of simulations for the image at a user-defined IF for use in further analysis.

Interaction Factor Plugin
From the Interaction Factor menu selection, choose the first option -Interaction Factor. A pop up screen will appear ( Figure 2).

Segmentation
Here, you select the options for the chosen ROI you want to see in the analysis. These include the following: 1. Channel 1(Ch1) Color-from a pull down menu one of three colors may be chosen (Red, Blue, Green) for the first channel 2. Channel 2(Ch2) Color-from a pull down menu one of three colors may be chosen (Red, Blue, Green) for the second channel 3. Threshold-from a pull down menu a threshold may be chosen. These are the standard ImageJ thresholds and additional information may be found at the ImageJ website.

Exclude Edge Clusters-the final options in this section is related to what information is
included in the ROI. When selecting the ROI, the line may cut through a cluster. You may choose to include or not include those clusters that are not completely within the ROI.
Once all the options have been chosen, click the button "Apply Overlay". All the clusters used in the analysis will be highlighted (in white) (Figure 4). If you wish to change any of the options then click the button "Clear Overlay". The selected clusters will be deselected but the ROI will remain unchanged.
You may then select new parameters in the Segmentation section. Figure 4. Example of zoomed-in image where clusters are outlined using the "Apply Overlay" button.

Note:
If the user has his or her own masks of the clusters created by another method, the user can still use the IF plugin by first combining the masks to an RGB image by going to Image -> Color-> Merge Channels and selecting channel 1 and channel 2 masks (make sure to uncheck the "Make composite" option). In the IF plugin select the Otsu threshold and continue to use the plugin normally.

IF Parameter
In this section, there is one parameter -'Move Ch1 Clusters' which is chosen by clicking the check the box (default). If this option is checked then, when calculating the IF, the simulations are going to be made such that Ch1 clusters will be placed randomly within the ROI. If the box is left unchecked, then Ch1 clusters will not be moved but stay in their current positions.

Additional Measurements
There are standard measurements displayed in the results table -the output from running an IF calculation. In addition to these, you may choose some other measurements you need to properly analyze your image. The scale is dependent on the resolution. For example, the scale for a super resolution image can represent 20nm. This number may be part of the metadata of the input image and is read by ImageJ when opening the image.

Output Options
There are several output options that may be selected as part of a run for further analysis of the results. Each option chosen will be displayed in a separate window. The possible selections include

Running the First Calculation
Once all the options are selected, you can execute the calculation by clicking the "Test IF" button in the lower right. A results window will be displayed.

Figure 5. Example of Results Table
The following is the data reported by the plugin: 1. Image-the number of the image used in the IF prediction. If there is an ROI ID, it will be added to the image name.

Scale-This is retrieved from the image meta data
For the next several columns, the IF and p-val are calculated with both Ch1 (Ch2-Ch1 IF) and Ch2 (Ch1-Ch2 IF) as the reference color. The reference color is the color for which the percentage of overlapping clusters is measured when calculating the IF (see manuscript for further explanation). A value of "NT" in the column value means "Not Tested" (these columns are included in case they are needed for future calculation).

IF-Interaction
Factor between two color clusters is a number between 0 and 1 where 0 indicates no interaction and 1 indicates complete interaction. Below is a guide for understanding the IF. If the number is in the "no or low interaction level" refer to the p-value. If the p-value is <0.02 this means that its likely there is an interaction between the clusters. In other words, if the p-value is <0.02 there is less than 0.02 probability that the percentage of overlaps observed are due to random occurrence. For an RGB image where Ch1 and Ch2 are chosen by the user as red (R), green (G), or blue (B).
Where th is the threshold determined by the thresholding method selected from the dropdown menu and ROI mask are the pixels inside the region of interest (ROI).

Running Multiple Calculations
You may execute multiple runs of the IF calculation with different input parameters and output images.
Each run is stored in the results table as a separate row. None of the outputs are destroyed between runs but are accumulated. If any options are changed in the Segmentation and IF Parameter sections, it may be advisable to save one "type" of run in a separate folder for comparison with subsequent runs.

The Final Run
Up until now each calculation was executed by clicking the "Test IF" button which kept accumulating Interaction Factor Simulations Plugin Figure 12. Interaction Factor Simulations Plugin displayed on your screen. If you decide not to execute the simulation then click the "Cancel" button.

Output
Each simulation will be displayed with the corresponding number at the end of the name. Figure 13. Example of Simulation Generated with IF = 0.90 Next, optional output masks will be displayed (refer to the previous section for details on the output masks). In addition, there will be a Results