ALEX Analysis

1. Overview

ALEX analysis is the latest step in the basic smFRET analysis workflow. It is also the first step before more advanced (sub-population) analyses of different kinds are performed on the data: shot noise analysis, burst statistics analysis, correlation, etc.

Note that, although the page is entitled "ALEX Analysis", data does not need to be acquired with alternated lasers (or multiple lasers for that matter) in order for many of the available tools to be usable. Single-laser smFRET data can be handled just as well, as will be discussed later.

2. ALEX Histogram

The ALEX Histogram graph (red box in the figure above) represents the stoichiometry ratio (S) of each selected burst versus its proximity ratio (PR) or FRET efficiency (E) histogram as an intensity plot. the 2-dimension histogram bin sizes and ranges are defined in the ALEX Settings tab of the Settings window, as discussed in the corresponding manual page.

The histogram can be calculated by clicking the ALEX Histogram button (Ctrl+L) and cleared by clicking on the Clear ALEX Histo button.

The exact nature of the represented quantities (E and S) depends on what kind of corrections is applied: no correction, background corrections, ALEX corrections, including or not gamma correction, etc.

The selected bursts depend on the Use Burst Analysis Constraints checkbox. If checked, these are the bursts verifying the constraints defined in the Burst Analysis page. If unchecked, all bursts defined during burst search are retained.

If the Keep ALEX 2D Data checkbox is checked, the burst data of previously analyzed data sets is kept. This is useful when analyzing low count sub-populations present in different data sets, or when pooling data from multiple spots in multispot analysis.

The ALEX Histogram is a LabVIEW Intensity graph object, whose functionalities should be relatively straightforward to understand.

Two cursors are provided, which allow defining a region of interest (ROI), used to select bursts in the ALEX Histogram (see the ROI Definitions section below for more information).

The color scale used to represent histogram counts can be changed using the Palette pull-down menu (and the Color Box control when a monochrome palette is selected).

Note that there are two small rectangular regions below and above the scale proper, which can be right-clicked and adjusted to a specific color used for any values below or above the maximum displayed scale range. In the example shown above, all empty bins (value < 1) are displayed in the "system" color. By default, this color would be identical to the palette color for the minimal value (here: black). To preserve this setting for future histograms, check the Fix Min Counts/Autoscale Max Counts checkbox (and keep the Autoscale Z lock in the unlocked position).

2 groups of indicators can be found to the right of the ALEX Histogram. They provide information on the ROI-selected bursts (if the Only Select Bursts in ROI checkbox is checked, see Section 4) or all bursts (if the checkbox is unchecked):

• # Selected Bursts: self-explanatory

• Total Duration (s): sum of all selected bursts durations

• E and dE: mean FRET and FRET standard deviation of all selected bursts

• S and dS: mean Stoichiometry Ratio and its standard deviation for all selected bursts

The latter values can be exported to the Gamma Analysis page for further analysis by clicking on the Store (E, S) button.

3. E and S Graphs

The E and S 1-dimensional graphs are located to the right of the ALEX Histogram (green box in the Figure above).

They can contain 3 types of plots described next.

3.1. Histograms

The 1D histograms are computed when the 1D ALEX Histograms (Histo) button is clicked. Either one (E or S) or both histograms are computed, depending on which checkbox below (E and S) is checked. The bin size used to compute these histograms is defined by the dE and dS controls below each graph.

3.2. KDE

Kernel Density Estimation (KDE) curves are computed when 1D ALEX KDE (KDE) button is clicked. Like for the 1D histograms, either one (E or S) or both KDE plots are computed, depending on which checkbox below (E and S) is checked. The bandwidth size used to compute these plots is defined by the KDE Bandwidth controls below each graph.

3.3. Fits

As for most graphs in ALiX, the right-click menu of the graph legend allows fitting any of the selected plots with a list of predefined models.

In addition to this capability, both graphs have a Fit button: Fit Last E Histogram (Fit E) for the E Histogram and Fit Last S Histogram (Fit S) for the S Histogram, which refer to the last compute histogram. These buttons can be used instead of the right-click menu, but are mostly intended to be used for scripting purposes. The model used to perform this scripted fit (or manually requested one) is selected in the a pull-down list of models next to it.

An additional feature of these graphs is the ability to right-click the plot area itself and select Show Fit Parameters. This contextual menu item displays the array of fit parameter names and values corresponding to the last fit. Using the menu item again hides the parameters.

As usual, the fit parameter values (as well as additional information on the fit) are automatically exported to the Notebook.

An important thing to remember about fits, is that they are limited to the part of the plot visible at the time the fit is requested.

In the example show below, the first fit (green curve) was performed using the range [-0.2, 1.2] for display, while the second fit (red curve) was performed using the range [0.2, 0.8] corresponding to the ROI boundaries defined in the ALEX Histogram graph. The first fit is obviously incorrect, while the second is clearly better.

4. ROI Definitions

A single shape (rectangle or oval, rotated by an arbitrary angle) can be defined in the ALEX Histogram graph using the cursors and controls located at the bottom left of the graph (blue blox in the Figure above). The usage of this ROI is described below.

4.1. ROI shape

The two cursors are used to define the bouding box of the non-rotated selected shape (rectangle or oval). To bring a cursor which is currently in a non-visible part of the graph, either right-click the cursor symbol in the cursor array (red crosses in the top Figure) and choose Bring to Center or type the desired coordinates to the right of the cursor symbol (X and Y columns).

The shape can be adjusted further by using the ROI Angle dial or typing a value in the corresponding numeric control (unit: degree (deg) or radian (rad)).

The display style of the ROI can be adjusted with the ROI Style, ROI Color and Line Width controls.

4.2. Burst Selection

The Only Select Bursts in ROI checkbox next to the ROI Definition parameters instructs the software to flag bursts within the ROI as "selected in the ALEX Histogram". If this checkbox is checked, returning to the Burst Analysis page and checking the Use ALEX-Selected Bursts Only checkbox will limit the analysis to the bursts which have been flagged. If the Only Select Bursts in ROI checkbox is unchecked, then performing the same set of actions will result in all bursts being selected (unchecking the Only Select Bursts in ROI checkbox amounts to resetting the "selected in the ALEX Histogram" of all bursts to "selected").

In other words, leaving the checkbox unchecked means that the ROI is not used and all bursts are used in the analysis. While it is correct to use a combination of Only Select Bursts in ROI unchecked checkbox and Use ALEX-Selected Bursts Only checked checkbox (in the Burst Analysis page), AFTER burst analysis has been performed, it does not make sense to check the Use ALEX-Selected Bursts Only checkbox before an ALEX Histogram has been computed, which is why this checkbox is automatically set back to False (unchecked) right after a Burst Search.

4.3. Labeling and Storing ROIs

To facilitate the repeated selection of sub-populations, it is possible to store ROI definitions by providing a name (ROI Label) for the currently defined ROI and storing it in the ROI List by clicking the Store ALEX ROI button ( + ).

To remove a stored ROI definition, select it in the list and click the Remove ALEX ROI button ( - ).

To use a previously stored ROI definition, select it in the list and click the Use ALEX ROI button.

The following 3 labels have a particular role in correction factors calculation (see following section): D-only, A-only and FRET.

5. Additional analyses

5.1. Single-laser smFRET data

While a meaningful stoichiometry ratio cannot be computed in the absence of an acceptor-specific laser excitation, application of the definition of S results in a value of 1 for this parameter. Computing an ALEX Histogram will result in a single color-coded line line in the ALEX Histogram graph. To obtain a 1D E Histogram, an ROI encompassing this line needs to be defined or simply unckeck the Only Select Bursts in ROI checkbox, and click the 1D ALEX Histogram button. Obviously, the S histogram will be limited to a single non zero bin and is of little use.

5.2. Shot Noise Analysis

Details about Shot Noise Analysis can be found in the corresponding manual page. We simply remind the reader that the 1D Shot Noise Analysis button (SNA) opens up the corresponding window (if it is not already opened) and copies selected bursts data for analysis in that window.

5.3. Correction Factors Calculation

Once the 3 special ROIs (D-only, A-only and FRET) have been defined, the Compute ALEX Corrections button (Corrections) is shown.

Pressing this button will trigger a different script depending on the type of data loaded in memory, based on the selection of specific sub-populations and estimation of diverse quantities.

For us-ALEX data, the D-only population is first selected and a linear fit of the F_D^A vs F_D^D scatter plot is performed. The computed slope provides an approximation of the D-leakage coefficient. In a second step, the A-only population is selected and a linear fit of the F_D^A vs F_A^A scatter plot is performed. The computed slope provides an approximation of the direct A-excitation coefficient.

For ns-ALEX data, related computations are performed using different nanotime histograms of the selected populations (unpublished and experimental).

The results of these different calculations are printed in the Notebook and can be used to update the correction factors used in further analysis.

5.4. Gamma Factor Analysis

As mentioned above, pressing on the Store (E, S) button will export the content of the (E, dE) and (S, dS) indicators to the Gamma Analysis page for further analysis. Consult the Gamma Analysis manual page for further details.