Nanotime Histogram Analysis

The Nanotime Histogram Analysis Window can be opened using the Ctrl-Shift-N shortcut or via the Windows>>Nanotime Histogram Analysis menu item.

It will also automatically open when requesting a fit from the Nanotime Analysis page in ALiX.

The function of the window is to fit nanotime decay histograms with a sum of exponentials convolved with an experimentally measured instrument response function (IRF).

The IRF is nothing but a nanotime histogram acquired in the proper conditions (not necessarily with the same settings as the nanotime histogram to be analyzed) and loaded in ALiX as described below.

The Nanotime Histogram to be fitted is selected in the Nanotime Analysis page of ALiX by right-clicking in the Fluorescence Decay Curves graph or its legend and selecting one of the two available options:

• Fit Nanotime Histogram (1 Plot)

• Fit Nanotime Histogram (2 Plots)

from the contextual menu appearing as shown below:

Fitting two plots simultaneously only makes sense if both fit share a parameter (for instance, a Donor and Acceptor decays in case of a FRET sample). We will first examine how the single plot fit functions in Section 1. Section 2 will cover the additional features of a 2 Plots fit.

1. Single Plot Fit

1.1. Selected Plots

By default, the window will open in the single fit mode, showing three tabs as indicated in the Figure below:

The Fitted Plot box indicates the type of curve currently studied. The complete list is available in the legend of the Fluorescence Decay Curves graph of the Nanotime Analysis page and is as follows (for ns-ALEX or TCSPC SPAD arrays):

• D-only F^D

• D-only F^A

• A-only F^D

• A-only F^A

• FRET F^D

• FRET F^A

When selecting one of these plots in the Fluorescence Decay Curves graph of the Nanotime Analysis page, the corresponding IRF (if it exists) will be automatically selected and displayed in the IRF box. For instance, for any F^D decay, the D-IRF will be used, while the A-IRF will be used for all F^A curves. If no IRF plot has been loaded and designed as such in the Nanotime Display page, this box will contain the correct IRF type, but attempting to perform a fit will result in the following error message:

Loading an IRF file and selecting the corresponding plot as the IRF will fix this problem.

1.2. Parameter Initialization

The next step consists in setting initial guess values for the fit parameters in the Fit Parameters (1 Plot) tab.

Note that none of these parameters can be equal to zero, due to the fitting approached used (Downhill Simple Minimization). Small values are fine as an alternative to a coefficient that is known to be close to or equal to zero. The fitted value should end up very close to zero.

Each line in the Decay Parameters array corresponds to one exponential decay component and is defined by an Amplitude parameter and a time constant, Tau (unit: ns).

To indicate that one of this parameter is fixed, check the checkbox to its right.

The scrollbar to the right allows showing more than the default 3 visible parameter sets (although it is not recommended to attempt fits with too many components).

The last line in the Fit Parameters tab shows the Baseline parameter and the Time Offset parameter (in ns). The baseline is simply the background value, while the time offset accounts for a possible temporal shift between the IRF and the fitted decay. Both parameters can be fixed by checking the checkboxes next to them.

In addition to these fit parameters, the fit is controlled by the Convergence Criterion and the Weighted Least Square option.

• The Convergence Criterion is the average chi-square difference between the simplex vertices and its center. The default value is fine for most applications

• Weighted Least Square is defining whether the chi-square quantity minimized during the fit procedure is weighted or not. The weight is the inverse of the fitted value at each point.

1.3. Starting the Fit

To start an iterative fit, press the Start button. The fit can be interrupted at any time by pressing the Abort button.

The current iteration step is indicated below the Current Convergence Criterion value.

The current fit parameters are indicated in the Decay Parameters set and the two Baseline and Offset indicators, each time the chi square of a vertex improves on the previous value. An updated fit curve is generated as well on these occasions.

The Convergence Criterion tab allows monitoring the progression of this parameter on a graph. Convergence criteria can be very large at the beginning, but they usually decrease exponentially. On occasions the convergence plateaus, but generally resumes after a while.

1.4. Computing Parameter Uncertainties

While the Simplex Downhill Minimization approach does not provide a direct way to estimate parameter uncertainties, it is possible to compute an estimate of these uncertainties (Phillips & Eyring, Anal. Chem. 60 (1988) 738-741). Pressing the Error Estimate button performs this calculation. The results are displayed in the Parameters Uncertainties (1 Plot) tab.

In some cases, the final simplex is not optimal to perform this estimation and the so-called quadratic approximation criterion is not met. A message will be displayed above the Error Estimate button. To get the estimated parameter uncertainties nonetheless, check the Ignore Quadratic Approximation Failure checkbox and press the Error Estimate button again.

Note: Starting with version 4.4.15, this option is set to TRUE by default and cannot be changed by the user.

It is possible to perform the error estimation automatically after the convergence criterion is reached by right-clicking on the Error Estimate button and selecting the Automatically Compute Error Estimate option. To revert to manual estimation, repeat the process to deselect the option.

To export the fit results to the Notebook (and the estimated uncertainties if they have been computed), press the Export button.

It is possible to export the results of the error estimation automatically after computation by right-clicking on the Export button and selecting the Automatically Export Results to Notebook option. To revert to manual export, repeat the process to deselect the option.

2. Double Plot Fit

To be added later.