Background

Background tab

The need for background correction

All raw DEER curves contain a (typically) exponential background originating from the random distribution of intermolecular spin pairs present in the sample. We are interested in the intramolecular (or intra-complex) dipolar interaction of spin pairs at relatively defined distances and thus need to correct for the background, leaving only the signal of interest. If the trace is very long, only background remains at longer times and it is easy to determine the shape of the background. Due to experimental limitations, this ideal case is often not possible to achieve but additional knowledge about the system allows us to recruit other criteria to check the validity of the background. Simple Tikhonov regularization can be used to judge how well the corrected signal can be represented as the Fourier transform of a sum of Pakes. If the suggested background is wrong, the resulting Tikhonov transform to the distance domain will show unrealistic excursions of positive and negative probabilities. If the background choice is correct, the distance transform will be near zero for long distances while the normalized running integral of the distance distribution will be nice and flat at a value of 1 at these locations. Deviations from this ideality can be used as a penalty function for automatic background determination as implemented here. It is still the responsibility of the user to pick the correct background model. Below are the detailed instructions for all background related operations.

This program contains three levels of background optimization based on the currently selected background model.

1. An instant background based on some reasonable assumptions. This is what we get whenever new data is loaded and before the background is further optimized. Typically, this estimate is already pretty good and can always be restored by clicking [Reset] here on the background tab. Resetting is useful whenever the background cursors have been manually moved to very unreasonable locations and will bring sanity back to the displays. The details of the algorithm is undocumented and involves a highly nonlinear weighted low order polynomial fit to the entire raw data.

2. A optimization based on the Tikhonov regularized distance distribution assuming that the real distances are limited to some range as described below and as carried out on the background tab. This method is often sufficient.

3. Co-fitting of the background parameters with model based or model free fits. This is carried out on the fitting tab after enabling "refine background". This method will give the highest background fidelity.

Zero Point

The zero point defines the position of the true zero time and needs to be accurate for a meaningful result. By default, auto shift is enabled (little check box, so you don't even need to click anything when coming from the “select” or “data” tab.) If you don't like the automatically determined zero value, you have several options. You can enter a numeric value (in nanoseconds, positive or negative) or you can simply move the green cursor. If you move the green cursor, hold down the <ctrl> key to zoom in for finer cursor control. While the cursor is moved, the back-calculated Tikhonov regularization is displayed as well as the difference to the data (red, see image) to guide the eye. The zero position is correct if the difference is flat. (It is recommended to use automatic zero determination, of course!) 

Auto selecting the zero point will not work if your data has a dead time (positive shift value, no data near time zero) and is thus truncated on the left, but you can still analyze such data by manually entering a positive value. Depending on the degree of truncation, the detailed analysis might show distortions. The default alpha (alpha=1) is typically fine but other values can be selected as needed, e.g. reduce alpha if the distance probability is very narrow or increase alpha if the data contains a lot of noise.

Background

Proper background determination is required to separate the interesting dipolar interaction between the two radicals from all other random inter-spin distances that exist in the sample. The detailed background depends on the geometry and many different models are available.

Model: Select the model (start with 3D, but you could later also try e.g. 3.5D. A higher value can for example partially correct for the excluded volume if you have a large protein where close distances are under-populated (compared to random) due to the presence of the protein). A background=none is useful for analyzing data that already has the background removed. It can also be used for regular data, but will cause significant distance probabilities at longer distances as expected.

The current background is shown as a blue line and is normalized to (1-modulation depth). This way it is is more intuitive to overlay it with the data, but note that the the background correction is actually a division. The math behind the scenes is correct.

The little graph in the lower part shows the Tikhonov regularized distance distribution. (Note that this looks different because negative probabilities are allowed. By default, the other Tikhonov regularization are non-negative). It also shows the running integral of the distribution in yellow. At this point we ignore the distortions and negative probabilities. To judge the quality of the background correction, we look at the longer distances (where there are no peaks left!). If the background selection is good, the purple data is close to zero and the yellow data is all close to 1 (more or less) above the dotted vertical line. You can grab the blue cursors defining the background and move the points up and down to see how things change and interactively improve the background. You can probably get close manually. Most models require 2 points to fully define the background. "VariableD" also requires a dimensionality and "Quadratic" will show 3 cursors as required. You can press [Auto Background] and have my algorithm optimize the background for you. The program guesses where the data peaks end and will place the vertical dotted white cursor at that distance before optimizing. If you know better, you can turn off "Auto Pos" and move that cursor where you think it should be before pressing [Auto Background] again. If the model is "variableD" You can manually set the dimensionality or have the algorithm optimize it for you. This will only work well if you have sufficiently long data. If the data is highly truncated you might be better off moving the cursors manually.  In highly truncated scenarios, there are additional systematic distortions and the distance data will not be exactly flat above the threshold. Users are encouraged to play with simulated data to get a feeling of the distortions in the presence of highly truncated oscillations.

If you have peaks at very long distances, go to the "internal data" tab and increase the upper distance limit (to e.g. 200A) to improve background determination. The “auto pos” is determined based on the integrated distance distribution, estimating where the integrated trace reaches a level of one. If the curve is initially highly distorted, you might have to press several times until the “pos” no longer changes. Just play around.

Note that the linear and quadratic models use a first or second order polynomial to the log of the Y values. A linear background will only look linear if you select the logarithmic display in the lower right.

NEW: The background can be defined by two different mechanisms: (1) the blue cursors, (2), the actual parameters for the background formula. You can change either one and the other will follow. For each background model, the parameters are shown as well as the formula defining them. All parameters that are used in the formula can be manually modified and the effect on the blue line observed. Three parameters are always shown, but only the ones actually used on the current model can be modified. For example, for a 3D background b3=3 is fixed and cannot be changed.

Notes: If the data is highly truncated, it is possible that the entire visible background is below the real data. In this case automatic background determination will fail. You can still manually move the cursors down until things look reasonable. If you run out of room to move the cursors down, increase the  "data offset" value on the lower right of the bottom graph (default is 2).

Fit Mode (experimental feature*).

There are three modes to optimize the background. (1) L, (2) H, (3) L&H (default). With "L", "find background" will try to make the distance distribution all zeroes above the threshold. For "H", it will try to make the integrated and normalized distance distribution all ones above the threshold. For "L&H", both criteria are applied simultaneously. It is recommended to leave this at the default.

Fitting data that is pure background:

Sometimes, a control experiment is carried out where it is known that there are no preferred distances (e.g. a singly labeled protein that remains monomeric and does not aggregate). This allows the determination of the background shape. The button "Fit Background Only Data" will fit the entire data to the background model. This way, e.g. the dimensionality can be determined more accurately and can then be kept fixed at that value for a similar system where specific dipolar interactions are present.

Modulation depth

The modulation depth calculated from the current background is displayed. (For most background models this is the same as 1-b1)

*To enable experimental features, go to the "Settings" tab and check the box.

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