Burst Statistics Definitions

2. Burst Selection Criteria

Two  types of constraints can be defined:

• Burst Statistics Constraints

• Number-limited Constraints

2.1. Burst Statistics Constraints

The first type of constraints is entered in the Constrained Statistics array (green box in the Figure above). 

An arbitrary number of those can be defined. Navigation in the array can be done using the index control (top right) or the scrollbar (bottom). The index control shown is that of the leftmost element shown.

Each Constrained Statistics is comprised of 4 components:

• the statistics definition: any valid statistics (basic burst statistics, alias or formula)

the statistics value range type: [Value 1, Value 2] or Value 1 +/- Value 2

• the range values: Value 1 and Value 2

When the Use Burst Statistics Constraints checkbox is checked, all definitions are used (an AND operation is used) to select valid bursts.

In order to use only a few constraints, it is not necessary to delete the unused ones from the array. Instead, uncheck the previous checkbox and specify which elements of the array to use in the Logical Combination of Constraints box (see below).

2.2. Number-limited Constraints

The second type of constraints is entered in the Number-Limited Constraints array (red box in the Figure above).

As for the previous array, an unlimited number of such constraints can be defined and the navigation principles are identical.

Each Number-Limited Constraint is comprised of 3 components:

• the number of bursts: N

• the type of number: Largest or Smallest (checkbox)

• the Statistics definition: any valid statistics (basic burst statistics, alias or formula)

As for the Burst Statistics Constraints, the Use N Largest/Smallest Statistics checkbox is checked, all definitions are used (an AND operation is used) to select valid bursts.

In order to use only a few constraints, it is not necessary to delete the unused ones from the array. Instead, uncheck the previous checkbox and specify which elements of the array to use in the Logical Combination of Constraints box (see below).

2.3. Logical Combination of Constraints

In order to only apply a few of the constraints defined in the two previous arrays, or to define more complex conditions, the Logical Combination of Constraints string can be used to define which constraints to use and how to combine them. An empty string applies no constraints (unless one or both checkboxes mentioned above are checked).

To define a valid logical combination, the following syntax elements can be used:

• Ci: i = 0, 1, ... NC-1, where NC is the number of constraints defined in the Constrained Statistics array.

• Ni: i = 0, 1, ... NN-1, where NN is the number of constraints defined in the Number-Limited Constraints array.

• logical operator: & (AND), | (OR) or ! (NOT)

• parentheses

 A simple example is shown in the Figure above, where the Constrained Statistics array contains 2 elements but only the first one is used.

Example of other valid expressions are:

• C0 & C1

• (C0 & !C1) | (N0 & !N1)

If an error is found in either the statistics definitions or the logical combination, a beep sound will be emitted and a warning message will be displayed in the box at the lower left corner of the window.

3. Applying Burst Selection Criteria

Once constraints have been defined, pressing the Burst Analysis (Ctrl-A) button (top left) will compute all needed statistics for all bursts found during the Burst Search step and select those which meet all constraints. The resulting number of bursts will be displayed in the # Burst Satistfying Constraints indicator (bottom of the page).

Note that the statistics will be computed using background corrections (either average or time-dependent) and/or ALEX corrections depending on which of the following checkboxes (top, middle) are checked:

• Background Corrections

• Use Time-Dependent Background Rates

• ALEX Corrections

Note that there is an additional Use ALEX-Selected Bursts Only checkbox as well. This option allows coming back to the Burst Analysis page after a first round of selection has been performed, followed by further selection of a subpopulation in the ALEX histogram. Pressing the Burst Analysis button again will now perform any requested action (in particular plotting histograms or scatter plot) on this subpopulation of bursts.

Warning: it is important to leave the Use ALEX-Selected Bursts Only checkbox unchecked when a Burst Search was just performed. Indeed, this generally clears up the ALEX histogram (unless specified otherwise) and the result of this selection will be that zero bursts will be found to both meet constraints defined on this page AND be selected in the ALEX histogram.

4. Definition of Burst Statistics Histograms and Other Plots

In addition to selecting bursts based on constraints, this tab is used to define optional plots which will be computed when the Burst Analysis button is pressed, and plotted in the different other tabs.

Note that some plots are computed and plotted without any intervention from the user, notably the burst duration and separation histograms and bursts number time trace and cumulative time trace. Parameters specifying these plots are defined in this tab and will be discussed below.

4.1. Burst Statistics Plots

If the Compute Burst Statistics Plots checkbox is checked, plots defined in the Burst Statistics Plots array will be computed when pressing the Burst Analysis button (see dark blue box in the Figure above).

The Burst Statistics Plots array is a list of valid statistics (basic burst statistics, alias or formula), associated with a Bin Size array, allowing to specify the size of each histogram's bin.

These histograms can be computed using logarithmically spaced bins if the Logarithmic Binning checkbox is checked.

When using a logarithmic binning the Bin/Decade parameter replaces the Bin Size array. An option to compute Sigworth & Sine representation of the distribution instead of the normal histogram is selected with the corresponding checkbox.

Instead of histogram, a Kernel Density Estimation (KDE) of the corresponding burst statistics can be computed by checking the KDE checkbox. Doing so replaces the Bin Size array by a KDE Bandwidth array, whose value can be specified for each different quantity. A typical usage of this feature is to first compute the histogram of a statistics using a specific value B of the histogram bin and next, to compare it with the KDE plot of the same statistics computed with a bandwidth W = B. Choosing a different bandwidth will result in plots scaled differently from one another.

Note that if the Bootstrap Error Estimate checkbox in the KDE Analysis tab of the ALiX Settings window is checked, each statistics' plot will result in bootstrap estimation, which may take some time...

4.2 Burst Duration & Separation Plots

The burst duration and separation plots are calculated each time the Burst Analysis button is pressed.

The parameters surrounded by a light blue box in the Figure above specify the type of plots computed, similarly to the parameters specifying the Burst Statistics plots discussed in the previous section. The Burst Duration Bin is the value used to bin the burst duration histogram (as well as the separation histogram). These histograms are plotted using units of seconds.

4.3. Statistics 2 vs Statistics 1 Scatter Plot

When the Statistics 2 vs Statistics 1 Scatter Plot checkbox is checked, a scatter plot representing the value of Statistics 2 versus the value of Statistics 1 for each selected burst. The two Statistics i Bin Size parameters are used to specify the binning of the corresponding 2D histogram visible in the corresponding tab.

Two options exist to compute this plot:

• Replace plot

• Add data to existing plot

The first one creates a new scatter plot each time the Burst Analysis button is pressed, while the second one adds the data points corresponding to the selected bursts to the previously plotted scatter plot. This option can be used to accumulate data from different files or different spots in the case of a multispot data file.

Finally, the Burst Index Delta parameter specifies which scatter plot is computed. Calling i = 0, ..., N the indices of the selected bursts, and d the value of the Burst Index Delta parameter, the plot represents Statistics 2(i+d) versus Statistics 1(i), for i = 0, ..., N--1. This parameter is useful to study memory effects in a series of bursts.

4.4. Busts Number Time Traces

The # Bursts Time Trace Bin parameter specifies the duration of the time trace window used to compute the number of selected bursts. The larger this parameter, the less point this curve will comprise, but the lower the parameter, the lower the number of burst per window will be counted (and the larger the variance of this quantity). A typical single-molecule sample with standard burst search and selection parameters will results in a few bursts per second.

5. Other Buttons

Four more buttons can be found at the bottom of this tab:

• Statistics Aliases: opens the Statistics Aliases Definitions window (see the corresponding page of the manual for information).

• Save Burst Statistics Definitions: saves the value of all controls in the tab to a .asd file which can be reloaded (and exchanged) for later use.

• Load Burst Statistics Definitions: loads an .asd file to restore all controls in this tab to a saved state.

• Export Burst Data: opens the Burst Data Export Options from which burst statistics can be exported into an ASCII file (see the corresponding page of the manual for information).