Static 2c FRET Data
The following section describes the workflow when analyzing static, 2-color smFRET (single-molecule Förster Resonance Energy Transfer) data. Deep-LASI provides a modular workflow for analyzing the data, either manually or automatically. The analysis starts with the co-localization of fluorescent molecules between both channels and trace extraction, the categorization process, the determination of correction factors, the selection of time windows to be analyzed per single time trace, the kinetic analysis, and ends with a summary of the analyzed traces by calculating the distribution of the correction factors, the FRET and stoichiometry values.
We describe how to use Deep-LASI for two examples: (1) a publicly available example data set published by Hellekamp et al., Nat. Meth (2018), which was recorded on a split camera, and (2) a static two-color DNA origami sample, which was recorded on two separate cameras. Further sample data sets can be found, e.g., in Wanninger et al., BioArxiv (2023).
Overview - Example 1
Example 1
Sample Design: Static Double-Stranded DNA
The first data sets are chosen from a multi-laboratory benchmark study. It contains two single-molecule data sets of double-labeled DNA molecules. The two samples feature a low (Fig. 49, left) and intermediate FRET efficiency (Fig. 49, right) by design, with the attached fluorophore pairs being separated by 23 and 15 base pairs, respectively.
Fig. 49 Double-Stranded DNA labeled with the donor dye Atto550 and acceptor dye Atto647N in 23 bp distance (left) and 15 bp separation (right).
Data preparation
The DNA molecules were recorded on a TIRF microscope with dual-view inset and alternating laser excitation at an exposure time of 200 ms (Fig. 50). To analyze the data, we downloaded the raw data from Zenodo and saved the raw .tif files for (1) the calibration measurement, (2) the low FRET sample and (2) the intermediate FRET sample.
Fig. 50 Alternation cycle and position of the two detection channels on the camera when using a dualview inset.
In the first step, we need to identify the detection channels, i.e., their position on the camera and the applied laser excitation schemes (Fig. 50). For this, we can, for example, use ImageJ to load any of the downloaded movies encoding the single-molecule data of the two DNA constructs. When looking at the tiff-stack with alternating laser excitation on a frame-to-frame basis, we can identify the detection channels best during the red excitation period: frames with red excitation show emission on the left half of the camera (acceptor emission after acceptor excitation), while no emission signal is observed on the right half of the camera (Donor emission after acceptor excitation) due to the missing excitation of the donor molecule. This means the donor emission after donor excitation (DD) is detected on the right half of the camera, while the acceptor emission after donor excitation (DA) or direct excitation (AA) is recorded on the left half of the camera. Furthermore, we can identify an ALEX cycle RG starting with red excitation R followed by yellow excitation Y for 1 frame each (Fig. 50).
Co-Localization of Molecules
Next, we need to know where double-labeled DNA molecules are detected on the two field-of-views (FOV) of the camera, i.e., which pixel on the red channel corresponds to a pixel on the yellow detection channel (Fig. 51). While differences in magnification will not be observed on a single camera, there can be still a slight tilt or shift between the two images due to the alignment of dual-view inset.
Fig. 51 Determination of the transformation matrix by mapping the donor on the acceptor channel.
To retrieve the transformation matrix, which translates single molecule localizations in one channel onto the other, we first used Deep-LASI to generate a map. For this, we loaded the calibration file calib20140402_0.tif into the software. In the first step (Fig. 52, A), we read in the data from the red channel (which is on the left half of the movie) into the first channel. For this, we loaded the movie via File > Mapping > Create New Map > 1st channel. Deep-LASI can handle input data with full or halved field-of-view. We chose the left half of the camera for the red data and confirmed. In the second step (Fig. 52, B), we loaded the data for the yellow channel via File > Mapping > Create New Map > 2nd channel and chose the right half of the camera.
Fig. 52 Workflow to create a map between both detection channels
After loading the file, Deep-LASI shows the averaged image for each detection channel separately and automatically detects single emitters (Fig. 52, C). The numbers of localization and potential mislocalization can be adopted using the slider below the two images. We chose Channel 1 (red camera) as a reference, i.e., Deep-LASI warps the image from the yellow channel onto the red detection channel.
The result is afterwards shown in a side-by-side image that depicts the overlay of both channels before and after the mapping (Fig. 52, D). Lastly, we saved the generated map via File > Mapping > Save Map.
Trace Extraction
After generating the transformation matrix via mapping or reloading the already generated map via File > Mapping > Load Prev. Map (Ctrl + M), we can load the actual single-molecule data in the next step. To obtain the trajectories of individual molecules depending on the laser excitation, Deep-LASI can detect and extract traces on a single file basis. For this, it can read single .tif files and save the extracted traces in separate .mat files, which can be added file-by-file afterwards for further analysis. However, Deep-LASI also permits extracting traces from raw data files with consecutive numbering. In the presented example, we proceeded by reading in all raw .tif files per experiment at once, i.e., the data files FSII1a_g30r84t200_0.tif until …_6.tif or FSII1b_g30r84t200_0.tif until …_6.tif for the ‘low-FRET’ and ‘intermediate-FRET’ sample, respectively. We loaded the data of the first channel (as specified during the mapping process) via File > Load Image Data > 1st channel for the red channel and selected the files.
Fig. 53 Settings for extracting the different emission channels depending on the excitation cycle.
Next, we specified the experimental settings for Deep-LASI (Fig. 53, A). We provided the interframe time of 200 ms, given by the exposure time and frame time together. Next, we specified the excitation cycle ‘RG’ by typing in the ALEX sequence.
Note
Due to coding reasons, Deep-LASI recognizes the letters B, G, R, and I as input for the laser excitation in the ALEX cycle. They are required for the correct selection of laser excitation cycle and visualization in multi-color experiments, later. Yellow excitation is also referred to as ‘green’ (G) excitation and infrared excitation is abbreviated with (I).
The ALEX sequence activates a slider that allows one to switch between the specified number of excitation sources and to observe in the image on the left whether the correct slider position is set. We chose the red excitation cycle by selecting the left position of the slider. Previously defined frame range is set automatically to the whole number of frames during the meaurement, and Limit particle detection, image frame range allows for omitting frames (at the beginning or the end) in case of measurement errors or other experimental settings. For reading in ALEX data in this example, we can read in all frames - ranging from 1 to the total number of frames, which is 1000 in the case of the ‘low-FRET’ sample and 1600 in the case of the ‘intermediate-FRET’ sample. Selecting the fluorophore in this study is optional and will provide additional metadata to the saved file containing the extracted traces. We finished the read-in process by selecting the red detection channel by pressing the R button (Fig. 53, A).
Note
While in 4-color FRET experiments, the channel order from 1 to 4 directly matches the detection channels, in 3-color or 2-color FRET experiments, in particular, there are different combinations of excitation and detection channels (BG, GR, RIR, BR, BIR, GIR) that will lead to an identical extraction of the single-molecule data as long as the corresponding ALEX sequence is given and matching the detection channels. The only difference is that Deep-LASI will choose different colors when displaying the traces afterwards. Deep-LASI will interpret the detection channels in the order of channels presented during the mapping process. For color consistency, we chose yellow/red excitation.
In the second step, we loaded the data of the yellow detection channel via File > Load Image Data > 2nd channel and selected the files. Next, we provided the experimental settings for the yellow channel (Fig. 53, B) leaving the specified interframe time of 200 ms and the excitation cycle of ‘RG’ unchanged.
We chose the yellow excitation cycle by selecting the right position of the slider and confirmed all frames 1-1000 (1-1600 in the case of the ‘intermediate-FRET’ sample). Having specified the fluorophore, we finished the read-in process by selecting the yellow detection channel by pressing the G button (Fig. 53, B).
In the following, Deep-LASI automatically reads the raw data file-by-file, localizes molecules in the acceptor channel, identifies molecules in the donor channel by mapping, and extracts the trajectories of every molecule found depending on the excitation cycle. This process is carried out iteratively for the number of files specified and can last several minutes. The progress of the extraction process is shown in the left corner of the GUI and allows one to guesstimate the waiting time. Once the extraction process is finished, the extracted traces would be saved in the data folder by the program, and in any later time the user can save the traces via File > Save Traces / State (Ctrl + S) to keep all the changes updated on the file.
Note
In case an error occurs, try to save the extracted traces anyhow. For some Windows installations test sofar, we encounter a GUI error at the end of the extraction process, which has no influence on the prior extraction process.
With the threshold settings that we used, we got in total 855 traces from the 7 data files for the ‘low-FRET’ DNA sample. The manual and automatic analysis steps and results are explained in the following section.
Manual data analysis and correction
By using the Navigation slider we clicked through all the traces one by one to check their individual features and attribute them to one or several categories created in the Classification chart. You can see the result of manual trace sorting on Fig. 54. For a detailed description of manual analysis steps please see the section Traces GUI.
Fig. 54 Categories manually created for the static two-color ‘low-FRET’ DNA sample
After categorization, we moved on to the Histograms tab to plot the results especially the apparent and corrected FRET efficiencies to compare them with the published results. For this, we first plotted and fitted correction factors as you can see on Fig. 55. For each of the plots, we chose the corresponding category from the Data Selection panel by clicking on the plus sign beside its name, followed by selecting the desired correction factor from the Plot Mode table. So, we first chose the category G Alpha and then on the Plot Mode, we clicked on Direct Excitation Factor (Alpha). For the Fit Method, we chose Gauss1, and clicking on Fit Plots, we got the plot with fitting results (Fig. 55, left). We took similar steps for the other two correction factors. So, we chose the category RR Beta for plotting Spectral crosstalk corr. factor (Beta), and RR Gamma for Detection efficiency corr. factor (Gamma) respectively. You can see the resulting plots and values for correction factors on the middle and right panels of Fig. 55.
Fig. 55 Correction factors plotted and fitted after manual categorization and region selection. From left to right, direct excitation, spectral crosstalk, and detection efficiency correction factors.
The values we obtained for correction factors for this published data set through manual analysis are 0.064 for the direct excitation, 0.077 for the spectral crosstalk, and 0.792 for detection efficiency.
Next, we plotted the FRET Efficiency histograms to get the final value for corrected FRET efficiency and calculate the distance between the two fluorophores. For this we selected the category Manual Selection which consists of all the traces with high enough quality for final analysis. Then we plotted apparent and corrected framewise FRET Efficiency on the Plot Mode respectively, and fitted the plots in each case. As you can see on Fig. 56, the apparent and corrected FRET efficiencies obtained via manual analysis are 0.22 and 0.18 respectively. Based on Hellekamp et al., Nat. Meth (2018), the corrected FRET efficiency is expected to be 0.15 ± 0.02, and the value of 0.18 that we got from the manual analysis is close enough considering the quality of traces. Using the reported \(R_{0}\) value of 62.6 Ao, we calculated the distance to be 80.6 Ao.
Fig. 56 Apparent and corrected FRET efficiency histograms with the fitting result after manual categorization and region selection
Automatic data analysis and correction
In the following section you will see the automatic analysis results for the static two-color ‘low-FRET’ DNA sample. For a detailed description of automatic analysis steps please see the section Automatic smFRET Analysis. We first need to have the traces loaded on the program, then from the Deep Learning tab, we clicked on Magic Button. The traces were categorized by the program as shown on Fig. 57. The resulting histograms and FRET efficiencies are reported on the following section.
Fig. 57 Categories created by Deep-LASI for the static two-color ‘low-FRET’ DNA sample
Plotting and Summary of Results
The first two plots created by Deep-LASI are the confidence level distribution for determining the number of states and states prediction with a tracewise manner resulting from the state classifier (Fig. 58).
Fig. 58 The Deep-LASI confidence level for determining the number of states and state values on traces
The next plot as shown on Fig. 59 is the FRET efficiency histogram based on observed states. At a first glance, it might seem that there are two FRET populations. This can happen because of the poor amount of statistics. If we could have more measured data, in the order of a couple thousands of single molecule traces for example, for sure the histogram will look more like consisting of only one FRET population.
Fig. 59 The histogram of apparent FRET efficiency averaged for each state
Finally, we get all correction factors as histograms with their mean, median, and mode values reported. As you can see on Fig. 60, the moleculewise direct excitation and spectral crosstalk are shown on the left and right panel of the figure respectively.
Fig. 60 The histograms of direct excitation and spectral crosstalk correction factors reported with statistics
Also the detection efficiency correction factor (gamma factor) calculated based on the mean, median, and mode values of direct excitation and spectral crosstalk factors is shown on Fig. 61. Comparing the resulting factors with what we obtained from manual analysis shows that the median values of correction factors are usually a better estimation for our data set.
Fig. 61 The histograms of detection efficiency correction factor reported with statistics
Having all correction factors, we can move on to the Histograms tab to plot the corrected FRET efficiency and accordingly calculate the distance between the dyes. So, choosing the category Static with 255 traces (Fig. 57), selecting the FRET Efficiency (corrected) on the Plot Mode panel, and setting the Histogram Type to be framewise, we continued with histogram normalization to Unary (Max = 1), and Gauss1 fitting. The resulting histogram is shown on Fig. 62.
Fig. 62 Corrected FRET efficiency histogram with the fitting result after using the Magic Button
Now, knowing that the corrected FRET efficiancy is 0.164, we can calculate the distance using the same reported \(R_{0}\) value of 62.6 Ao. Using the FRET efficiency-distance formula, the distance between the dyes was calculated to be 82.12 Ao. The FRET efficiency and calculated distance are within the range of reported values on Hellekamp et al., Nat. Meth (2018).
One can conclude that in the case of this published data set, the automized Deep Learning approach gives a more accurate result compared to the published value than manual analysis. It could be due to the fact that, especially in case of more noisy traces, manual analysis is done with some error in recognizing the correct bleaching steps or region selection to build up the correction factors and FRET efficiency histograms. Deep-LASI can give a more acceptable final result based on the more exact analysis approach of frame-wise correction factors determination.
Overview - Example 2
Example 2
Sample Design: Static L-Shaped DNA Origami
The described data set in this section is from smTIRF measurements of 2-state DNA origami structures as shown on Fig. 63. The origami is labeled with Atto488 (donor) and Atto647N (acceptor) which are both attached to the origami structure. The flexible tether, which can freely bind to single-stranded binding sites (on 6 and 12 o’clock positions) has a 8 nt, 1 mismatch overhang, and should not affect the energy transfer between the two fluorophores.
Fig. 63 L-shaped DNA origami structure labeled with Atto488 and Atto647N. The tether that can freely move around and bind to either of the two binding strands should not have an effect on the energy transfer between the blue and red dyes.
Data preparation
The origami structures were measured on a smTIRF microscope with two separate EMCCD cameras, one for the donor and one for the acceptor. ALEX with a BR excitation cycle was used to excite the donor and acceptor fluorophores alternatively at an exposure time of 50 ms, also the frame transfer time of the cameras was set to 2.2 ms. The resulting data would then be videos of consecutive frames from each channel with .tif file format. You can find a couple of raw data movies on Zenodo.
Co-Localization of Molecules
When using two separate detection paths like the present example, there might be the chance of some discrepancy between the cameras’ fields of view resulting from chromatic and spherical aberrations or cameras misalignment regarding to shifts, rotation, or magnification difference. To make sure that double-labeled species are detected, a correct linking of same molecule emitters across the detection channels is needed. Deep-LASI makes a coordinate transformation map to get rid of any potential difference. For more details about mapping, please refer to the section Mapping.
To perform the mapping step, we used zero-mode waveguide (ZMW) as a calibration pattern which was illuminated by the wide-field lamp on the microscope. The ZMW was then imaged on both channels and with the steps shown on Fig. 64, we opened the images one by one and used them to calibrate both channels. You can take the same steps as we did with the following instructions.
Fig. 64 Workflow to create a map between both blue and red detection channels
We loaded the ZMW image from the blue channel through File > Mapping > Create New Map > 1st channel. On the opened window (Fig. 64, A), we clicked on Full and OK. We took similar steps to open the ZMW image from the red camera. So after loading the file via File > Mapping > Create New Map > 2nd channel (Fig. 64, B), and checking the pattern on the preview, we clicked on Full and Horizontal Flip, and confirmed.
After loading the files, Deep-LASI shows the averaged image for each detection channel separately and automatically detects single emitters (Fig. 64, C). The numbers of localization and potential mislocalization can be adopted using the slider below the two images. We chose Channel 1 (blue camera) as a reference, i.e., Deep-LASI warps the image from the red channel onto the blue detection channel. The result is afterwards shown in a side-by-side image that depicts the overlay of both channels before and after the mapping (Fig. 64, D). Lastly, we saved the generated map via File > Mapping > Save Map .
Trace Extraction
After the mapping step, we can load the actual single-molecule data in the next step. Since Deep-LASI permits trace extraction from raw data files with consecutive numbering, to obtain the trajectories of individual molecules depending on the laser excitation, we proceeded by reading in all raw .tif files from the experiment at once. For more details about trace extraction, please refer to the section Trace extraction. We loaded the data of the first channel (the blue, as specified during the mapping process) via File > Load Image Data > 1st channel and selected all the files.
Next, we specified the experimental settings for Deep-LASI. We provided the interframe time of 52.2 ms, given by the exposure time (50 ms) and frame time (2.2 ms) together (Fig. 65, A). Next, we specified the excitation cycle ‘BR’ by typing it in the ALEX sequence box. On the activated slider, we chose the blue excitation cycle by selecting the left position of the slider. Previously defined frame range is set automatically to the whole number of frames during the meaurement, but for Limit particle detection, we started the frame range from the 2nd one, because in our setup for the cameras triggering adjustments, the first frame is always a dark one. We finished the read-in process by selecting the blue detection channel by pressing the B button (Fig. 65, A).
Fig. 65 Settings for extracting the different emission channels depending on the excitation cycle.
In the second step, we loaded the data of the red detection channel via File > Load Image Data > 2nd channel and selected the files. Next, we provided the experimental settings (Fig. 65, B) leaving the specified interframe time of 52.2 ms and the excitation cycle of BR unchanged. We chose the red excitation cycle by selecting the right position of the slider, and finished the read-in process by selecting the red detection channel by pressing the R button.
then, Deep-LASI automatically reads the raw data file-by-file, localizes molecules in the donor channel, identifies molecules in the acceptor channel by mapping, and extracts the trajectories of every molecule found depending on the excitation cycle. This process is carried out iteratively for the number of files specified and can take a while.
With the threshold settings that we used, in total 7758 traces were extracted from the 99 data files for the DNA origami sample. The manual and automatic analysis steps and results are explained in the following sections. To avoid repeating the same explained analysis steps, we explain the different cases only
Manual data analysis and correction
By using the Navigation slider we clicked through the first 2500 traces one by one to check their individual features and attribute them to one or several categories created in the Classification chart. For a detailed description of manual analysis steps please see the section Traces GUI.
After categorization, we moved on to the Histograms tab to plot the results especially the apparent and corrected FRET efficiencies. For this, we first plotted and fitted correction factors. For each of the plots, we chose the corresponding category from the Data Selection panel by clicking on the plus sign beside its name, followed by selecting the desired correction factor from the Plot Mode table. So, we first chose the category R Alpha and then on the Plot Mode, we clicked on Direct Excitation Factor (Alpha). For the Fit Method, we chose Gauss1, and clicking on Fit Plots. We took similar steps for the other two correction factors. So, we chose the category BR Beta for plotting Spectral crosstalk corr. factor (Beta), and BR Gamma for Detection efficiency corr. factor (Gamma) respectively. Unfortunately, with 2500 traces, there were not enough statistics for the correction factors due to the noisy data set, and also unstablitiy of Atto488 dye. So, one has to click through all traces to get better histograms, but for the sake of time, we used the advantages of Deep-LASI to obtain the correction factors, and FRET efficiency as you can see on the following section.
- warning:
If the complete manual analysis is needed for this data, please let me know:)
Automatic data analysis and correction
In the following section you will see the automatic analysis results for the static two-color DNA origami sample. In case you are interested in more details about automatic analysis, please check the section Automatic smFRET Analysis. After loading all the traces on the program, from the Deep Learning tab, we clicked on Magic Button. The traces were categorized by the program as shown on Fig. 66. The resulting histograms and FRET efficiencies are reported on the following section.
Fig. 66 Categories created by Deep-LASI for the static two-color DNA origami sample
Plotting and Summary of Results
The first two plots created by Deep-LASI are the confidence level distribution for determining the number of states and states prediction with a tracewise manner resulting from the state classifier (Fig. 67). As you can see the occurence on the y axis on both graphs, having more than 1 state in the data set is negligible, and it means that we have one state, as we expected based on the DNA origami strucure.
Fig. 67 The Deep-LASI confidence level for determining the number of states and state values on traces
The next plot as shown on Fig. 68 is the FRET efficiency histogram based on observed states. It shows a broad distribution of apparent FRET efficiencies around the value 0.6. This broad distribution could be due to the rather high level of noise within the current data, and it can lead to false state detection during the analysis.
Fig. 68 The histogram of apparent FRET efficiency averaged for each state
Finally, we get all correction factors as histograms with their mean, median, and mode values reported. As you can see on Fig. 69, the moleculewise direct excitation and spectral crosstalk are shown on the left and right panel of the figure respectively.
Fig. 69 The histograms of direct excitation and spectral crosstalk correction factors reported with statistics
Also the detection efficiency correction factor (gamma factor) calculated based on the mean, median, and mode values of direct excitation and spectral crosstalk factors is shown on Fig. 70.
Fig. 70 The histograms of detection efficiency correction factor reported with statistics
Having all correction factors, we can move on to the Histograms tab to plot the corrected FRET efficiency. So, choosing the category Static with 304 traces (Fig. 66), selecting the FRET Efficiency (corrected) on the Plot Mode panel, and setting the Histogram Type to be framewise, we continued with histogram normalization to Unary (Max = 1), and Gauss1 fitting. The resulting histogram is shown on Fig. 71.
Fig. 71 Corrected FRET efficiency histogram with the fitting result after using the Magic Button