SUBTRACTION ... by Robert P. Rambo, Ph.D.

Scatter offers a buffer subtraction routine that uses, as input, normalized integrated intensities. Normalized implies each I(q) has been corrected for exposure time and beam fluctuations. The normalization is typically performed by the instrument or beamline during data collection.

Scatter offers several strategies for performing a buffer subtraction. At B21 (Diamond Light Source), data is collected as a series of 1 second exposures. Each 1 second exposure is written as a normalized 3 column text file. For a one minute exposure, we will get 60 frames that must be merged before used in a subtraction. Merging can be performed by either averaging (from Average Buffer) the set of buffer exposures or taking the median (from Median Buffer) value for each I(q). The median offers resistance to outliers in the dataset, however at 60 frames, the average and median should converge. Files are loaded by dropping the appropriate *dat file in either the "SAMPLES" or "BACKGROUND" panel.

Figure 1:

After loading a set of buffer files, you can look at the average and median of the sets by clicking on "Average and Median". The plots should be very similar; however, if you have very few buffers, the median tends to be the better choice.

In Figure 2, I loaded a set of files from a size-exclusion couple SAXS experiment. Before doing the subtraction, I would like to use the SAXS curves corresponding to the peak elution. We can quickly calculate and plot the frames corresponding to the peak by clicking on "Signal Plot". This will estimate a signal (see below) for each input SAXS curve. In addition, if you would like to overlay the Rg for each curve, then click on the checkbox (Add Rg to Signal Plot). Note, adding Rg to the plot will take some time as a subtraction and autoRg is being performed for each dataset.

Figure 2:

The signal plot in Figure 3 shows a peak forming between frames 12 and 25. This would correspond to the frames with maximal scattering intensity; however, the Rg (cyan) calculated for each frame is nearly constant across the entire sample set. Using the mouse, I can select the region of interest for subtraction and merging (Figure 4). Merging can be through averaging the selected set or by taking the median. If you are subtracting and merging a set of SEC SAXS curves or curves that differ by concentration then you must check "Scale then Merge" before doing the actual subtraction.

Figure 3:
Subtraction_fig_5 Figure 4:

"Scale then Merge" (Figure 2) will scale the data to a reference dataset. The default reference dataset is the first file in the selected sample set, however, you can specify the reference using the dropdown menu.

Before the actual averaging of the subtracted (normalized) datasets, Scatter will standardize the data and determine the variance for each bin, if a datapoint falls outside of the cut-off based on the variance scaled by the cut-off, the datapoint is rejected from the final dataset used in averaging.

Alternatively, you can merge the data by calculating the median (Subtract from Median checkbox). This should only be applied to datasets at the same concentration as no prior scaling can be applied. This method works well for repeated measurements of a dilute sample where the signal if very weak at high q-values.

Unsubtracted SAXS Signal

A SAXS measurement of your macromolecule is really a measurement of two: 1) the buffer(background) scattering and 2) the background plus particle(s) scattering. Consequently, the SAXS profile of the particle, under dilute conditions, is determined as the difference between the scattering of the two samples. Therefore, it is absolutely essential that the buffer environment between the two samples match as closely as possible with the only difference due to the particle(s).

Figure 1:

Figure 1 shows the same buffer measured at two exposures: 300 (left) and 1 (right) seconds. Clearly, the variance of the signal is greatly reduced in the 300 second exposure, particularly in the high q region (q > 0.1). Overlaid in each, is a sample measurement at 1 second exposure. As you can see at q > 0.2, the differences are small if not negligible and it would be difficult to assert that the differences observed at q > 0.2 for both 1 sec (right) exposures is meaningful.

Figure 2:

We can assert that information is present by taking the ratio of the intensities of the sample (particle+background) to the background. Assuming an ideal buffer matching, the presence of signal would be indicated by a ratio greater than 1 (Figure 2). Clearly, in the low q region, a significant peak exists suggesting the presence of a strong signal that decays towards a constant baseline. The peak is an artifact of the instrument and suggests, to the left of the peak, the signal is decaying (likely due to scattering from the beamstop). In the high q region (right panel), a significant fraction of the ratio > 1, suggesting information is present albeit weak. We can use this plot as a means of detecting a SAXS signal that does not require buffer subtraction nor a determined Guinier region. It can be expected that the area under the ratio plot (integral) will scale with concentration and particle mass. Therefore, for a set of SAXS curves collected during an size-exclusion chromatography (SEC) run, a plot of the integral of the ratio for each SAXS measurement will generate a trace of the elution peak.