Single-Spot Tutorial 3: us ALEX Shot Noise Analysis

To execute this tutorial, the following files are needed:

• 004_dsDNA_17d_green100u_red40u.hdf5

• ALiX Settings & Controls 17d Single-Spot usALEX Analysis.txt

These files can be found on Figshare at:

• https://dx.doi.org/10.6084/m9.figshare.1098961

• https://dx.doi.org/10.6084/m9.figshare.3839427

Start ALiX if it is not running already. Remember that multiple copies of ALiX can be run in parallel (but be aware of memory limitations if you analyze large files). It is recommended to open the Notebook (Windows >> Notebook or Ctrl+N) at this stage, but this is not mandatory and can be done at any time during the analysis. Information regarding all steps are stored internally and sent to the Notebook in the order they were generated, the first time it is opened).

1. - 8. Load File - ALEX Analysis 

The first few steps of this tutorial are identical to those of Tutorial 1: us ALEX FRET Analysis (in fact Shot Noise Analysis - SNA - can be viewed as the last step of us ALEX FRET analysis). Please refer to this tutorial and follow its steps 1 through 8 before moving to step 9 below.

Note: It is not necessary to perform a fit of the E or S Histogram (or even compute the E or S histograms for that matter) in order to perform SNA. However, SNA is complementary to these analyses, therefore it is usually a good idea to compare the results of these analyses to those of SNA.

9. Shot Noise Analysis using a FRET Distribution Model

• Press on the SNA button to open the Shot Noise Analysis window and transfer the currently selected burst data to it (Note 1).

From this step on, all actions are performed in the Shot Noise Analysis window unless mentioned otherwise.

• Switch to the E Histogram panel of the Shot Noise Analysis window and adjust the histogram bin dE to the desired value. The value specified in the loaded script (0.02) is fine, and so would the value used to compute the E Histogram in ALiX (0.03).

• Check that the Model and its parameters (displayed on the left hand side of the window are as shown below:

• Select the Analysis >> Simulate Shot Noise menu item (Ctrl+S) in the SNA window.

This starts a simulation of the shot noise effect on data characterized by the selected burst size distribution and a Gaussian distribution of FRET efficiency E. The N = 5 parameter indicates that N times the number of selected bursts (# Bursts) are used in the simulation.

The results is a simulated histogram (SNA) plotted against the original histogram (E Histo) in the E Histograms graph, and the corresponding residuals (Histo - SNA) plotted in the E Histogram Residuals graph (Note 2):

The relatively good match between simulation and original histogram indicates that the simulation parameters are close to optimal, and in particular that there is some FRET efficiency dispersion. For a better estimation, optimization can be used, as described next.

• Switch to the Optimization Parameters tab and make sure the current parameter values are defined:

• Select the Analysis >> Optimize Parameters menu item (Ctrl+O). After a few minutes, the optimal parameter set is indicated in the left hand side of the panel, and a representative simulated histogram computed. in the E (and S) Histograms graph:

• Switch to the E MSE Map tab to see the optimization raw data. The location of the detected minimum is indicated by a white dot in the figure below. Due to the noise of the mean square error, a potentially better guess of the minimum location is indicated by the green cursor (note however that the difference between the two values is minimal):

10. Shot Noise Analysis using a Distance Distribution Model

A similar analysis can be performed using a distance distribution model instead of a FRET distribution.

• Change the Model parameter to Rod+Linkers.

• Set the FRET Parameters to the following values:

• • Run a simulation (Analysis >> Simulate Shot Noise or Ctrl+S). The resulting E Histograms should look something like this:

• Use the Analysis >> Convert Simulation Parameters/Plot p(E) (Ctrl+P). After a little while, the following results are displayed:

Notice that the <E> and SDV(E) values are similar to those obtained as an optimal choice in the previous analysis using a p(E) distribution.

• Switch to the FRET Distribution panel. The E Distribution corresponding to the r and s parameters of the Rod+Linkers model is plotted. Its first statistical moments are those shown above,

To optimize the parameter values, go through the following steps.

• Switch to the Optimization Parameters tab and make sure the current parameter values are defined:

• • Select the Analysis >> Optimize Parameters menu item (Ctrl+O). After a significantly longer time than for the E distribution model (5 hrs in our lab), an optimal parameter set is indicated in the left hand side of the panel, and a representative simulated histogram computed. in the E (and S) Histograms graph. To obtain the corresponding E distribution statistics, use Analysis >> Convert Simulation Parameters/Plot p(E):

• Switch to the E MSE Map tab to see the optimization raw data. The location of the detected minimum is indicated by a white dot in the figure below. Due to the noise of the mean square error, a potentially better guess of the minimum location is indicated by the green cursor (note however that the difference between the two values is minimal):

The most likely optimum appears to be the set used as a guess at the beginning of this section.

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Congratulations! You just completed Single-Spot Tutorial 3:  us ALEX Shot Noise Analysis.

Notes

(1) Opening the Shot Noise Analysis window via the Windows >> Shot Noise Analysis menu does not transfer the currently selected burst data to the SNA tool. This is done by pressing the SNA button in the ALEX Analysis page of ALiX.

(2) The SNA histograms are normalized so that their area equals that of the original histogram. This results in a smoothing of the simulated histogram as the number of replicas (N) increases.