Shot Noise Analysis

• Use ALEX Correction Factors

         The ALEX correction factors used are those defined in the ALEX Corrections page of the ALiX Settings window.

• Background Corrections

          If checked, background counts are simulated, using fixed background count rates as defined in ALiX.

• Use Time-Dependent Background Rates

          If checked, time-dependent background counts are simulated, using variable background count rates as defined in ALiX.

It is important to remember that any correction settings (background correction, other corrections) defined and selected in the ALEX Settings and 

ALEX Corrections pages of the ALiX Settings window will be applied when computing the E or S Histograms from the simulated data.    

Obviously, it makes sense to:

1. either Compute corrected data and represent them with correction applied,

2. or Compute uncorrected data and represent them uncorrected. 

2.4. Performing the simulation

To perform the simulation, use the Simulate Shot Noise (Ctrl+S) item of the Analysis menu.

Depending on the number of requested simulations and the number of bursts, this can take some time to execute. 

The result, an average E (and S) histogram, will be displayed in the E Histograms and S Histograms graphs (shown on their respective E Histogram and S Histogram page) as a SNA plot, shown as a light grey histogram superimposed onto the original (observed histogram) in the figure above. These histograms will be calculated with or without applying corrections depending on whether the Use ALEX Corrections Factors checkbox is checked or not in the  ALEX Corrections page of the  ALiX Settings window.

2.5. Results

The residuals (difference between observed and computed histograms) will be displayed in the E (or S) Histogram Residuals graph underneath the main histogram graphs. Residuals can be normalized (i.e. divided by the value of the original histogram - or 1 if the histogram value is 0) by checking the Normalized Residuals checkbox.

The average mean squared error of the N simulated histograms and corresponding standard deviation will be displayed as E <MSE> (or S <MSE>) and E MSE SDV (or S MSE SDV). These quantities are computed with or without weighting, depending on whether or not the Weighted Least Square checkbox (in the Optimization Parameters tab) is checked. The SDV values will decrease as N increases, but the calculation will also last longer. Moreover, the histograms will be smoothed out by averaging and differ markedly from the observed histogram.

2.6. p(E) Statistics

In the case of the Rod+Linkers Model, the (r, s) parameters can be converted into the corresponding p(E) distribution statistics by using the Convert Simulation Parameters/Plot p(E) (Ctrl+P) menu item of the Analysis menu. The resulting p(E) Statistics will be displayed on the main panel (red box in the figure below), and the corresponding FRET distribution represented in the FRET Distribution graph of the FRET Distribution tab.

Note that this computation can take some time (due to the different statistical moments involved in the Converted FRET Parameters computation).

For the Gaussian (Truncated) Model, this action computes the  p(E) Statistics and displays the actual p(E) curve used in the analysis.

3. Optimizing model parameters

While it is possible to try out different pairs of parameter until the observed residuals (or <MSE>) appears optimal, a more systematic approach can be used with the set of controls provided in the Optimization Parameters tab (Figure below).

These parameters define the min and max values of the each parameter of the model as well as the increment used during the search:

• <E> (<E>_min, <E>_max) and Sigma E (Sigma E_min, Sigma E_max) for the Gaussian (Truncated) E distribution model (increments <E>_step, Sigma E_step).

• r (r_min, r_max) and s (s_min, s_max) for the Rod+Linkers E distribution model (increments r_step, s_step).

In addition to the Weighted Least Square checkbox discussed previously, two other checkboxes are visible: E Histogram LS and S Histogram LS. They indicate which quantity will be used to find the optimal set of parameters (E least square or S least square, or the sum of both if both are selected)

To start an optimization, use the Optimize Parameters (Ctrl+O) item of the Analysis menu. A progress bar will indicate the amount of calculation remaining, while the result of each parameter set estimation will be shown on the respective graphs (E and S Histograms and Residuals). It is possible to abort the calculation at any time by pressing on the Abort button which will appear during optimization.

After the calculation is completed, the optimal parameter set is used and the results displayed in the respective graphs. The cursor is moved to the optimum location.

Two Mean Square Error (MSE) maps can be examined in their respective tab (E MSE Map and S MSE Map). The figure below shows an example of such a map (corresponding to the settings shown on the figure above).

In this particular case, the minimum is obtained for the pair (r, s) = (0.85, 0.052), using corrections.

• Use Smoothed Map option and Smoothing parameter

Because the MSE maps are noisy, the absolute minimum might not be located where the theoretical minimum is.

To improve the situation, it is possible to apply some Gaussian blur (or smoothing) to the map.

This is controlled by the degree of smoothing (the number of time a 3x3 Gaussian blur is applied to the map before finding the minimum is attempted).

These settings are specific to each map and independent.

Changing either of this parameter automatically updates the map.

The new minimum location can be obtained by right-clicking the map and choosing Find Minimum.

4. Options

Shot Noise Analysis options are defined in the Shot Noise Analysis page of the Settings window (this window can be opened using the Windows >> Settings (Ctrl+E) menu item. The following options are available:

• Use ALEX Correction Factors

When checked, the us ALEX Correction Factors defined in the ALEX Corrections page of the Settings window are used to compute random burst replicas.

This is a different option than the Use Other Corrections and Correction Type = us ALEX found on that other page, which are used to compute corrected histograms. However, as explained in the Shot Noise Analysis manual page, both are usually used in conjunction (both on or both off).

• Keep Burst Data

When checked, bursts data (including associated background rates) are stored in memory within the Shot Noise Analysis window, in order to globally analyze multiple series of bursts (for instance, in a multispot experiment).

When the SNA button in the ALEX Analysis page is pressed, the data of selected bursts is copied and passed to the SNA window. As such, it is possible to perform SNA analysis on bursts while doing other data analysis in the main ALiX window.

When checking the Keep Burst Data checkbox, each new set of bursts data is added to, rather than replace, the previous bursts data set stored for SNA. Associated with this bursts data set is the set of background corrections used with the bursts (average or time-dependent).

This feature allows several bursts data set to be pooled, histogrammed and analyzed as a whole, which is useful for multispot experiments, for instance.

Note that when performing simulations on pooled data, each simulated burst is associated with its respective background correction (if corrections are used), but the same set of ALEX correction parameters is used for all data sets.

• Optimize Parameters when New Data Arrives

When checked, new bursts data sent from the ALEX Analysis page are processed automatically (or queued if one is already in progress).

This option is useful when scripting. For instance, this allows sequentially processing multiple pairs of channels corresponding to multiple spots in a multiple spot experiment. If a multiple spot script is run in ALiX, with a call to the 1D Shot Noise Analysis action for each spot, each spot's selected bursts in the ALEX histogram will be independently analyzed.

• Convert Parameters when Modified

When checked, the E statistics (and p(E) curve) are automatically computed each time the model parameters are modified.

Since this computation can be time consuming in the case of the Rod + Linkers model, it is recommended not to check this box unless these statistics are needed. This option is mostly useful when scripting.

• Output to Notebook

When checked, shot noise analysis results are automatically output to the Notebook.

Note that during parameter optimization, the shot noise simulation results are automatically silenced, therefore it is not necessary to check off this option for that specific purpose.

The typical use case for this option is during manual exploration of the parameter space. Turning off Output to Notebook avoids crowding the Notebook with intermediate results of little interest.

The Export Graphs to Notebook and Verbose Mode options of the General Settings page of the Settings window applies to outputs of the Shot Noise Analysis window. However, Graphs are only exported at the end of an optimization. To export a Graph to the Notebook at a different time, use the context menu Copy Data function and paste the result in the Notebook.

• Export to Origin after Optimization

When checked, optimization results are sent to Origin (OriginLab, version 8 and above) automatically (see details below).

In order to avoid overwriting previously exported data, the root name of the export folder is incremented for each new data set. For instance, if the root name is Book, the second data set results will be exported in a folder called Book (2), etc.

The worksheet, matrices and graphs created in the process have names starting with the root name provided in the box to the left of the button. They are placed in a new subfolder of the active project folder, the subfolder having the root name provided in the text box (default: Book1).

After this export process, Origin's active folder is restored, which allows repeating this action and create a series of subfolders at the same hierarchical level in an Origin project.

Note that at this time, due to a bug, Origin needs to be closed from the Task Manager, as LabVIEW doesn't properly release the Origin application reference.