Automated Two-dimensional Spatiotemporal Analysis of Mobile Single-molecule FRET Probes

1. Software prerequisites

1. Install the miniconda Python distribution²⁷ (minimum required Python version: 3.7).
2. Open an Anaconda prompt in the Windows Start menu, or open a terminal and execute conda activate if using Linux or macOS.
3. Enable the community-maintained conda-forge package repository²⁸ by executing the following commands:
   conda config –add channels conda-forge
   conda config –set channel_priority strict
   conda update –all
4. Install the required Python packages by executing:
   conda install opencv trackpy lmfit ipympl scikit-learn pyqt sdt-python jupyterlab
5. Become familiar with JupyterLab, the user interface of the analysis software (refer to the software documentation²⁹).
6. Install the git version control system, which will be used later to download and update the analysis software. If using Linux, use the distribution's package management software to download and update. Otherwise, execute:
   conda install git
7. Optionally install the sidecar Python package to display datasets after filtering steps during analysis:
   conda install sidecar

2. Measurement of samples

Figure 1: Image Acquisition. (A) Excitation sequence. After recording an optional image of a dye-loaded cell using the 405 nm laser, donor and acceptor are excited alternately and repeatedly for illumination time t_ill using 532 nm and 640 nm lasers, respectively. The time t_r between donor and acceptor excitation must be long enough to allow for image readout by the camera. The delay time t_delay can be used to adjust the acquisition frame rate and, therefore, the observation time span before photobleaching. This panel is modified from ¹⁶. (B) Fiducial markers are used for the calculation of the coordinate transforms between the two emission channels. Matching fiducials are indicated by color. Several shifted images should be recorded to ensure that the whole field of view is covered. (C) Laser profiles for flatfield correction are recorded using a densely labeled sample. The acceptor profile is recorded and photobleached, followed by acquisition of the donor profile. Multiple images should be taken at different sample regions, averaged, and smoothed to mitigate the influence of sample imperfections (e.g., the bright spot in the center-top of the image). (D) Flatfield correction map p(x,y) calculated from 20 laser profile recorded as described in C. Abbreviations: FRET = Förster resonance energy transfer; Im_DD = donor emission image upon donor excitation; Im_DA = acceptor emission image upon donor excitation; Im_AA = acceptor emission image upon donor excitation. Scale bars = 5 µm. Please click here to view a larger version of this figure.

1. When using an electron-multiplying charge-coupled device (EMCCD) camera, enable the EM gain to observe single-molecule signals at high signal-to-noise ratios (refer to the manufacturer's instructions).
2. Excitation sequence (see Figure 1A for further details).
   1. Optionally record an image for segmentation to restrict data analysis to certain regions in the field of view. For instance, excite Fura-2-loaded cells using a 405 nm laser and capture their emission around 510 nm to evaluate only probes located in interfaces between cells and supported lipid bilayers (SLBs). Consequently, wait for time t_r to permit camera readout.
      NOTE: On EMCCD cameras, t_r depends on the number of lines in the chosen region of interest (ROI). Therefore, choosing a small ROI can be advantageous because it reduces the delay between frames and the size of recorded data. Additionally, enabling frame transfer mode allows for further reduction of t_r.
   2. Alternately excite donor and acceptor fluorophores repeatedly.
      1. Excite the donor for an illumination time t_ill (5-10 ms is typically short enough to avoid motion blur) while also triggering the camera.
      2. Wait for time t_r to permit camera readout.
      3. Excite the acceptor for while triggering the camera.
      4. Wait for a time t_delay.
         NOTE: This must be longer than t_r to enable readout by the camera but can otherwise be chosen arbitrarily. It shall balance the requirements for time resolution and trace length.
      5. Repeat steps 2.2.2.1-2.2.2.4. Choose the number of repeats to be large enough to ensure photobleaching of at least one fluorophore per probe within the field of view, which permits stepwise photobleaching analysis for discrimination of single-molecule signals from aggregates.
         NOTE: Choosing appropriate t_ill and excitation laser intensities commonly requires some experimentation: The longer the illumination times and the higher the laser intensities, the better is the signal-to-noise ratio in the resulting images, but the shorter are the resulting time traces.
3. Record a sufficient number of movies for each sample.

3. Additional measurements for the determination of correction factors

1. Record a series of randomly placed fiducial markers visible in both emission channels for image registration (i.e., finding the transformation that maps coordinates of the donor emission channel onto the acceptor emission channel and vice versa). See Figure 1B.
   NOTE: Image registration is performed by the software; see step 6.1.4.
2. Measure the intensity profile for both donor and acceptor excitation light sources for flatfield correction (i.e., correcting for inhomogeneous excitation across the field of view). To this end, prepare a sample featuring a high density of FRET probes and first acquire an image upon acceptor excitation, followed by photobleaching of the acceptor and subsequent recording of an image upon donor excitation. For increased stability, repeat several times in different sample regions. See Figure 1C,D. Alternatively, record a sample decorated with only the donor molecule and a second sample decorated with only the acceptor fluorophores.
   NOTE: Flatfield correction is performed by the analysis software; see step 8.1.2.
3. Record a single-molecule sample (as in section 2) of a probe without an acceptor fluorophore to determine donor emission leaking into the acceptor channel.
   NOTE: Donor leakage can also be computed from the actual probes' time traces after acceptor bleaching. If a sufficient number of such events is recorded, no additional measurement is necessary. Both options are supported by the analysis software; see Supplemental Information, section 3.15.
4. Acquire recordings of a probe without a donor fluorophore for the quantification of direct acceptor excitation by the donor excitation light source.
   NOTE: Direct acceptor excitation can also be derived from the actual probes' time traces after donor bleaching. If a sufficient number of such events is recorded, no additional measurement is necessary. Both options are supported by the analysis software; see Supplemental Information, section 3.15.
5. Record a single-molecule sample featuring two distinct FRET efficiencies to correct for differing detection efficiencies of the donor and acceptor emission channels and differing quantum yields of the dyes.
   NOTE: Such samples could be, for instance, Holliday junctions¹, which fluctuate between two conformations, or DNA rods that have FRET pairs attached at different, well-defined distances. If probes feature high and sufficiently constant FRET efficiencies, the correction can also be computed from acceptor bleaching events of probes' time traces, in which case no additional measurements are necessary. Both options are supported by the analysis software; see Supplemental Information, section 3.15.

4. Single-molecule localization algorithms

NOTE: Several analysis steps require single-molecule localization. Choose between a Gaussian fitting algorithm³⁰ and center-of-mass computation³¹, depending on signal density, background, and signal-to-noise ratio.

1. To perform Gaussian fitting, choose the 3D-DAOSTORM³⁰ algorithm via the respective user interfaces.
   NOTE: 3D-DAOSTORM is designed to distinguish even signals with overlapping point spread functions. While this is generally an advantage, it comes with a caveat: single, bright signals are occasionally identified as two adjacent ones, which can confuse the tracking algorithm and result in the detection of two short trajectories instead of a single long one.
   Set the following parameters (for details, see the documentation of the sdt-python library³², which provides the algorithm's implementation).
   1. radius: Set the initial σ value of the Gaussian fit function in pixels depending on the effective pixel size.
   2. threshold: Set a minimum amplitude (i.e., brightest pixel value, corrected for the estimated local background) for a local intensity maximum to be fit.
      NOTE: The threshold is arguably the most important parameter. If set too low, noise may be considered a fluorescence signal, and bright signals may be fitted with two Gaussians. If set too high, dim signals are not fit.
   3. model: Set to 2d to fit circular Gaussians.
      NOTE: The other models are not applicable to the smFRET data.
   4. find filter: Apply a filter before finding local maxima to reduce noise, which is helpful in low signal-to-noise ratio situations. This can be i) identity: no filter; ii) Crocker-Grier: bandpass filter from Crocker-Grier algorithm^31,33; or iii) Gaussian: a gaussian blur with σ set by the sigma parameter.
      NOTE: For Crocker-Grier, the feat. size parameter should be roughly the radius of a point spread function in pixels.
      NOTE: Fitting is performed using unfiltered raw data.
   5. min. distance: Fit two prospective signals separated by fewer than min. distance pixels by a single Gaussian.
      NOTE: This can help in the aforementioned scenario where a bright signal is wrongly detected as two adjacent signals.
   6. size range: Select minimum and maximum σ of the fits to remove detections from spurious signals due to noise.
2. Choose the Crocker-Grier algorithm via the respective user interfaces to perform center-of-mass computation (a refined algorithm³¹ based on Crocker's and Grier's idea³³).
   NOTE: This algorithm is very robust even in low signal-to-noise scenarios and in dealing with signals featuring a range of intensities but cannot fit molecules with overlapping point spread functions precisely.
   1. radius: Set the radius (in pixels) of a disk large enough to contain the whole point spread function.
   2. signal thresh.: Set the minimum amplitude (brightest pixel above estimated background) for a local intensity maximum to be analyzed.
      NOTE: If set too low, noise may be considered a fluorescence signal. If set too high, dim signals are not fit.
   3. mass thresh.: Set the minimum total intensity (sum of background-corrected pixel values) of a signal to be analyzed.
      NOTE: Same considerations as above apply.

5. Software initialization

1. Download analysis scripts. In an Anaconda prompt, navigate to a folder to save the analysis (using the cd command) and execute
   git clone https://github.com/schuetzgroup/fret-analysis.git target folder
   1. Replace the target folder with a descriptive name such as 2021-06-14_Force-FRET-experiment.
      NOTE: The analysis software will end up in this folder; ensure that this folder does not exist beforehand. It is recommended to download a copy of the analysis scripts for each experiment. This way, it is possible to revisit the analysis later, recall the parameters used, and make changes.
2. Copy Jupyter notebooks (01. Tracking.ipynb, 02. Analysis.ipynb, 03. Plots.ipynb) into the newly created folder (henceforth referred to as the root folder). If this is the first time using the software, get them from the notebooks subfolder of the root folder.
   NOTE: If similar datasets have already been analyzed, copying the notebooks from a previous experiment can be a convenient option, as parameters may have changed only slightly.
3. Start the JupyterLab server by executing the following command in the Anaconda prompt to open a web browser window displaying JupyterLab.
   jupyter lab
   NOTE: The browser is only the interface, while the process running in the Anaconda prompt is doing the actual work. As a consequence, closing the browser window has only minimal effect; the session can be restored by accessing http://localhost:8888. However, interrupting the JupyterLab process in the prompt or closing the prompt will terminate the analysis, leading to the loss of unsaved work.
4. In the JupyterLab browser window, use the left pane to navigate to the root folder. Double-click on 01. Tracking.ipynb to launch the first notebook. After launching, look for a new tab to appear, which displays boxes, so-called cells, of Python code.
   NOTE: All Jupyter notebooks feature comments describing the functionality of each code cell. Additionally, documentation for every method call can be displayed by placing the text cursor immediately before the opening ( and press Shift+Tab.
5. See Figure 2 for an overview of the data analysis process.

Figure 2: Overview of a typical analysis pipeline. Note that filtering steps are subject to adaptation according to the experimental design. This figure is modified from ¹⁶. Abbreviation: FRET = Förster resonance energy transfer. Please click here to view a larger version of this figure.

NOTE: Sample data to try out the software can be downloaded from https://github.com/schuetzgroup/fret-analysis/releases/tag/example_files

6. Localization, tracking, and fluorescence intensity analysis of single molecules (01. Tracking.ipynb).

1. Use the 01. Tracking.ipynb Jupyter notebook for the reliable analysis of fluorescence intensity values of single-molecule signals, which is tailored for the precise quantification, particularly of faint signals often occurring in FRET measurements (e.g., due to low donor signals at high FRET events and vice versa).
   NOTE: To this end, direct integration of the pixel intensities in the raw data with correction for the local background is implemented. For screenshots of each analysis step and description of function call parameters, refer to the Supplemental Information.
   1. Specify the illumination sequence to permit the selection of donor and acceptor excitation frames, as well as frames for image segmentation from recorded image sequences.
      NOTE: As the software allows the processing of data recorded with arbitrary illumination protocols, it is necessary to indicate which frame in an image sequence was acquired while exciting what type of fluorophore; see Supplemental Information, section 1.2, step 3. The frame numbers of the original image sequence are preserved.
   2. Describe and load datasets. Analyze multiple datasets at once, provided they were recorded using the same illumination settings. Assign an identifier and a pattern that matches the respective image sequence file names to each dataset. Additionally, define specific datasets for special purposes, such as recordings of fiducial markers for image registration, excitation light profiles for flatfield correction, and optionally donor-only and acceptor-only samples to determine correction factors.
   3. Select emission channels in raw images if both channels were recorded using a single camera. For this, use the appropriate graphical widget to select the appropriate regions for donor and acceptor emission.
   4. Localize fiducial markers in both emission channels and perform image registration. Use the provided user interface to find the appropriate parameters for the localization algorithm for both the donor and the acceptor emission channels. See section 4 for information about supported localization algorithms.
      NOTE: Randomly distributed fiducial markers can be identified across emission channels by the spatial distribution of their nearest neighbors (Figure 1B). A custom implementation of the algorithm proposed for selective plane illumination microscopy³⁴ in the sdt-python library automatically matches the position of each marker in the donor emission channel with the position in the acceptor emission channel. A transformation T mapping the donor emission channel's coordinates to the acceptor emission channel's coordinates is found via a linear least-squares fit of an affine transformation to the markers' positions³⁵. RANSAC is used to account for outliers, such as wrongly matched positions from the previous step.
   5. Localize FRET probes independently upon donor and acceptor excitation in all frames and merge results into one table that contains the original frame number, 2-dimensional coordinates, and an identifier referring to the source image file.
      NOTE: To this end, the software provides user interfaces to find appropriate options for the localization algorithm.
      1. Localize FRET probes upon donor excitation in the sum of the images obtained from donor emission Im_DD and acceptor emission Im_DA, which hardly depend on the FRET efficiency. For information concerning the options for the localization algorithm, see section 4.
         NOTE: Each sum image is calculated by transforming Im_DD using the transformation T previously obtained from image registration and added pixelwise to Im_DA.
      2. Localize probes upon acceptor excitation in the acceptor emission channel Im_AA (see section 4 for details about the localization algorithms).
   6. Perform tracking and fluorescence intensity measurement.

Figure 3: Single-molecule intensity measurement. (A) For a fluorophore located at the orange pixel, its uncorrected intensity I_uncorr is determined by summing up all pixels' intensities within a disk (yellow and orange pixels) large enough to cover all pixels affected by the signal: . The local background is computed as the mean of the pixels in a ring (blue pixels) around the disk: , where n_ring is the number of pixels in the ring. The fluorescence intensity I is the result of subtracting the background from the uncorrected intensity, I = I_uncorr – b × n_disk, where n_disk is the number of pixels in the disk. The circle radius is specified via the feat_radius parameter of the tracking method. The width of the ring is given by the bg_frame parameter. If the point spread function of one signal overlaps with the background ring of another (bottom panel), the affected pixels (red) are excluded from local background analysis. If two point spread functions overlap, fluorescence intensities cannot be calculated reliably and are therefore discarded. (B, C) Simulations show that applying a Gaussian blur with a standard deviation of 1 pixel improves the signal-to-noise ratio up to a factor of close to 2 at low fluorescence intensities (B) and introduces hardly any error (slight underestimation of less than 1%, (C))¹⁶. Moreover, the relative error (i.e., (I_meas – I_truth)/I_truth, where I_truth is the ground truth and I_meas is the outcome of the analysis) is constant over the whole intensity range and therefore cancels out for ratiometric quantities such as FRET efficiencies and stoichiometries. All plots are based on previously published work¹⁶. Abbreviations: SNR = signal-to-noise ratio; FRET = Förster resonance energy transfer. Please click here to view a larger version of this figure.

1. Choose appropriate options for the trackpy³⁶ algorithm used to link FRET probe localizations into trajectories. In particular, set the maximum search distance from one frame to the next and the number of consecutive frames for which a signal may go undetected, which can occur due to bleaching or missed localizations.
   NOTE: These gaps are filled via interpolation between preceding and ensuing positions. These interpolated positions are marked and only used later for reading out intensity values but not for diffusion analysis. Tracks are analyzed in the coordinate system of the acceptor emission channel. For fluorescence intensity analysis (step 6.1.6.2), tracks are additionally transformed to the coordinate system of the donor emission channel using the inverse transformation T^-1 obtained via image registration (see step 6.1.4).
2. Select options for the fluorescence intensity calculation algorithm (see Figure 3A for details). Specify i) the radius of a disk that, when centered on a signal's position, contains all pixels affected by that signal and ii) the width of a ring around each disk used to determine the local background.
   NOTE: To reduce noise in the obtained intensity measurements, a Gaussian blur with a standard deviation of 1 pixel is applied to the images (Figure 3B,C).

7. Use the analysis software functionality to process auxiliary image data from image sequences.
   1. Extract additional images recorded to facilitate segmentation (see step 2.2.1, marked by s in the excitation sequence (see Supplemental Information, section 1.2, step 3).
   2. Determine donor and acceptor excitation light profiles across the field of view from images recorded on a densely labeled sample (see step 3.2).
      NOTE: The pixel-by-pixel mean is calculated from the images to compute the light profiles. The camera baseline is subtracted. Images are blurred using a Gaussian filter to reduce effects due to sample impurities. Finally, the resulting images are divided pixelwise by their maximum value to get the profile p(x,y) mapping coordinates onto the interval [0,1].

7. Visualization of FRET trajectories (optional)

1. Use the inspector application to display single-molecule tracks in raw image data and the corresponding fluorescence intensities and apparent FRET efficiencies and stoichiometries.
   ​NOTE: This is a valuable tool to assess the validity of chosen parameters and manually accept or reject individual time traces. See Supplemental Information for a screenshot and detailed usage information.

8. Analysis and filtering of single-molecule data (02. Analysis.ipynb)

1. Use the 02. Analysis.ipynb Jupyter notebook for analysis and filtering of the single-molecule data obtained via the 01. Tracking.ipynb notebook. See the steps below for a typical analysis pipeline.
   NOTE: Different scientific questions and experimental designs may require adjustments of the settings. The use of Jupyter notebooks permits easy adaption by omitting, rearranging, and amending analysis steps. For screenshots of each analysis step and description of function call parameters, refer to Supplemental Information.
   1. Perform initial filtering steps.
      1. Discard signals with overlapping point spread functions as it is difficult to determine their fluorescence intensities reliably.
      2. In the case of inhomogeneous illumination, accept only signals located in well-illuminated regions within the field of view to ensure a good signal-to-noise ratio.
      3. If studying intramolecular FRET, restrict the analysis to those trajectories present from the beginning of the image sequence to ensure that all bleaching steps are recorded and can be properly evaluated later during the stepwise photobleaching analysis.
         NOTE: When performing experiments with intermolecular FRET probes, wherein donor and acceptor fluorophores are not part of a preformed complex, it may not be feasible to restrict the analysis to initially present trajectories.
   2. Execute flatfield correction, which uses the excitation light source profiles obtained in step 6.1.7.2 to reverse the position-dependent fluorescence intensity variations caused by inhomogeneous illumination.
      NOTE: The fluorescence intensity I(x,y) of a probe at the position (x,y) is corrected via ; see Figure 1C,D.
   3. Compute the apparent FRET efficiency E_app (i.e., the fraction of energy transmitted from the donor fluorophore to the acceptor fluorophore) and the apparent stoichiometry S_app (i.e., the number of donor fluorophores divided by the total number of fluorophores within a diffraction-limited spot).
      NOTE: By plotting E vs. S for each data point, it is possible to distinguish alterations in the measured FRET efficiencies due to change in donor-acceptor distance from alterations due to changes in the stoichiometry¹⁸. This allows for the differentiation between E = 0 due to dye separation from E = 0 due to the absence of an active acceptor. E-S plots are used throughout the analysis as a tool for quality assessment; see Figure 4 as an example.
   4. Perform stepwise analysis of photobleaching for the discrimination between single-molecular probes and aggregates. Choose to accept one of the following options.
      NOTE: To this end, the analysis software applies a custom implementation³² of the changepoint detection algorithm PELT³⁷ separately to the fluorescence intensity upon donor excitation (I_DD + I_DA) and acceptor excitation (I_AA).
      1. Choose option 1, wherein the acceptor fluorophore bleaches in a single step while the donor shows no partial bleaching (i.e., there is no bleaching step to non-zero intensity).
         NOTE: This option further rejects trajectories where the donor bleaches before the acceptor in a single step. Option 1 is the preferred choice in case of high acceptor photobleaching rates.
      2. Choose option 2, wherein the donor bleaches in a single step while there is no partial acceptor bleaching.
         NOTE: This option further rejects trajectories where the donor bleaches after the acceptor in a single step. Option 2 is the preferred choice in case of high donor photobleaching rates.
      3. Choose option 3, wherein either fluorophore bleaches in a single step while the other does not partially bleach.
         NOTE: Option 3 gives higher flexibility than options 1 and 2 and would be the suggested preference for data analysis.
      4. Choose option 4, wherein donor and acceptor fluorophores show single-step photobleaching or no photobleaching at all.
         NOTE: Option 4 is preferred in case of low photobleaching rates.
   5. Calculate the correction factors for donor emission leakage into the acceptor channel α, direct acceptor excitation δ, detection efficiencies γ, and excitation efficiencies β¹⁷.
   6. Use the correction factors to calculate the FRET efficiency E from the apparent efficiency E_app and the stoichiometry S from the apparent stoichiometry S_app.
   7. Perform further filtering steps. Select only data points from before the first bleaching event in each trajectory. Additionally, accept only trajectories with at least 75% of data points satisfying 0.35 < S < 0.6 to restrict the analysis to single-molecule probes (numbers are adjustable).
      NOTE: The upper and lower bounds for should be chosen according to the spread of the population of interest versus the populations to be excluded from the analysis (e.g., donor-only and acceptor-only populations). Based on experience, 0.35 < S < 0.6 turned out to be a good choice for many experimental situations.
   8. Perform image segmentation via global or adaptive thresholding methods³⁵ on the appropriate auxiliary images (see steps 2.2.1 and 6.1.7) to restrict the analysis to distinct regions within the field of view.
      ​NOTE: This permits, for instance, exclusive evaluation of probes located in a cell-SLB interface or on a patterned structure.

9. Plotting of results and further analysis (03. Plot.ipynb)

NOTE: Refer to Supplemental Information for screenshots of the Jupyter notebook and description of function call parameters.

1. Create E-S plots to verify that signals of incorrect stoichiometry have been correctly identified and removed.
2. Plot histograms of FRET efficiencies to provide a well-established overview of the FRET efficiency distributions. Group the histograms for convenient comparison of results from different experiments.
3. Evaluate the data further (e.g., diffusion analysis, conversion of FRET efficiencies to forces in experiments using molecular force sensors or transition analysis) within the notebook taking advantage of scientific Python libraries.
   NOTE: Data can also be exported in many file formats as input to other analysis software.