This US-SOMO module was conceived for the analysis of HPLC-SAXS data. In the image above, the main panel of the HPLC-SAXS module is shown. The buttons with the black labels are the ones currently active, the ones with the red labels become active when allowed by the processing/visualization stage. The graphics panel shows a collection of HPLC-SAXS log10[I(q)] vs. q SAXS data frames (points with 0 or negative values are automatically omitted from the visualization only) for a chicken egg-white lysozyme chromatographic separation on a Agilent BioSec-3 (3 μm particle size, 300 Å pore-size) 4.6 × 300 mm column, eluted with Hepes 50 mM, NaCl 100 mM, pH 7. Note the permanent upturn at very small q-values, due to biological material aggregated by the intense X-ray beam on the capillary cell walls under these far from optimal experimental conditions. While this kind of problem should be (and has been) preferentially dealt with at the experimental level, we use this dataset to demonstrate the potential for correcting data still presenting such an issue.
The left side of the window is divided in three sections, labeled "Data files", "Produced Data", and "Messages". By clicking on these labels, the corresponding panel below each label will disappear, allowing for an expansion of the remaining other panel(s). If every panel is made to disappear, the main graph will expand to cover the full size of the HPLC-SAXS window. By clicking again of the labels, the corresponding panels will be restored.
On the top left panel (Data files) there are four buttons:
The Add files button is used to load data into the module. An operating directory can be pre-selected by clicking on the path shown above it, and navigating in the file system (selecting the Lock checkbox will fix that directory). The file format for SAXS data recognized by the US-SOMO HPLC-SAXS module consist of .dat files with two or three TAB- or space-separated columns containing the q, I(q), and optionally their associated standard deviation (SD) values, respectively. Each frame number (or time value) must be present somewhere in the filename with a common prefix and suffix. For example, data1saxs.dat, data2saxs.dat, data3saxs.dat will be recognized as frames 1,2,3, where "data" and "saxs" can be replaced by any common sequence of characters. Consequently, 1.dat, 2.dat, 3.dat would be acceptable, but abc1.dat, qrs2.dat, xyz3.dat would not, because the prefix characters are not common. Furthermore, the loader will also arrange the data files sequentially, in increasing frame number (or time value) order. Concentration-related data should be instead uploaded using the Concentration load button (see below). I(q) vs. q and concentration data frames are automatically recognized and the labels on the x- and y-axes are then properly set.
Similar will select files with similar names and allow manual pattern matching entry if no new similar files are selected.
Concentration will show every file listed together with their associated concentration (mg/ml), if appropriate and properly set (see below). Concentrations can also be entered and modified manually. They can be used to normalize the I(q) vs. q data (see below). Loaded files can be displayed on the graphics panel by individually clicking on them (shift-click will select a contiguous series, ctrl-click allows multiple irregularly spaced selections). Produced data will also show up in this panel with associated putative filenames.
Remove files will discard previously selected files (see below); if the files were produced by the module, and were not previously saved, a warning window will pop-up, allowing to proceed or to stop removing the selected items.
Several buttons are available in the panel below the loaded files window:
Sel. all will select all files.
Sel. Unsel. will allow toggling the selection between selected files and everything else not currently selected.
Adv. Sel. will open up a panel in which several selection options can be utilized (see here).
View, active when up to ten datasets are selected, will show them in text format.
Movie: Pressing this button will open a pop-up window with the commands allowing to view in the main graphics window of the US-SOMO HPLC-SAXS module a series of selected data files in a movie-like manner, and to optionally save each frame as an image for real movie-making operations (see here).
The Log X (Lin X) and Log Y (Lin Y) buttons allow to toggle between linear and log10 scaling of the data on the x- and y-axes, respectively (if zero or negative values are present, they will be temporarily removed when the scale is set to log10 mode, as they cannot be shown on the display in this mode). The buttons will change their respective label once pressed, to underscore what is the action currently available.
Selecting the Err checkbox, active when up to 10 files are selected, will switch their representation from the dots connected with a line mode, to symbols (diamonds) with their associated SDs represented as error bars mode.
Rescale adjusts the X-Y axes on the graphics window to maximize the display of selected datasets (no effect on the data themselves).
Normalize will divide the I(q) data by the stored/entered concentrations.
Average will produce an average with propagated SDs of selected data. The I(q) values from each frame will be averaged, and then a scaling factor will be determined for each frame against the average resulting frame. The scaling factor for each original frame multiplies the frames's SD. The average intensity SD's are computed as the square root of the sum of the squares of each curves scaled SD's, and this is divided by the number of curves. The resulting datset filename will contain the number of frames averaged, and the initial and final frame numbers, followed by "_avg".
To SOMO/SAS will transfer selected datasets back into the US-SOMO SAS panel.
Each time the Width button is pressed, it increments the data line (or symbol) size of the plots, until it goes back to the initial value.
Color shifts the colors used in the graphics window; the operation can be repeated until a better contrast with the background is achieved. Note that the background color can be changed by right-clicking on the plot borders, which will open up a pop-up dialogue panel where all plot characteristics can be modified.
Bin allows averaging adjacent points in I(q) datasets, starting with the first point in the file and using a binning size defined in a pop-up dialogue:
Smooth performs a regularization of selected data using a moving window, whose dimension is defined in a pop-up menu (shown below), using a Gaussian smoothing kernel of 2n+1 points.
SVD opens a pop-up window were a single-value decomposition analysis (e.g., Williamson et al., Biophys J. 94, 4906-4923, 2008) can be performed on the selected data (see here). Important: the data must be all on the same grid; if not, a warning message will appear in the bottom left Messages window: "SVD: curves must be on the same grid, try 'Crop Common' first" (see below for the use of the Crop Common button).
Make I(t) is one of the crucial operations in the HPLC-SAXS module. It allows to generate a series of "chromatograms" (I(t) vs. t, where t can be real elution time or frame number) for each q-value present in the original data files (see below). A test could be automatically performed each time an I(q) vs. q dataset is converted into an I(t) vs. t dataset to ascertain if any I(t) vs. t "chromatogram" contain useful data, on the basis of a comparison between the signal and its associated SDs, by selecting its relative checkbox and the SD factor in the Options menu accessible from the button provided at the bottom of this window (see here).
Test I(t) Checks the I(t) vs. q selected curves to see if any fail the negative region test as described above.
Make I(q) is the other crucial operation in the HPLC-SAXS module. It allows to re-generate I(q) vs. q files for each frame after data treatment in frame- (or time-) space.
Concentration load is used to upload any chromatographic data files containing a concentration-related elution profile, such as those produced by UV-VIS absorption or refractive index detectors (the program will then internally keep track of such datasets, distinguishing them from SAXS datasets). By default, the program will look for "*.txt" files, but the choice could be expanded to other extensions in the file upload dialogue. The currently recognized format for concentration data is similar to the SAXS data format with the addition of the string "Frame data" in any place on the first line. The two or three columns of data are the frame number, concentration-related data, and optionally an associated SD value.
Repeak is used to effectively scale data (usually a concentration-related chromatogram) on the y-axis to a pre-set target (usually a low-q, high-intensity I(t) vs. t chromatogram), selectable in a pop-up window among the data subjected to this operation (this affects the data, a new file is generated with "rp" and the scaling factor added at the end of the filename). See more below on this subject.
Set will set an already uploaded and currently selected file containing the UV or refractive index profile vs. time or frame number as the source of the concentration-dependent signal.
Detector will allow to select the type of detector and to enter its calibration constant in a pop-up window (see here).
Since a typical HPLC-SAXS experiment produces a series of I(q) vs. q data collected at some time interval ("frames"), they can be inserted in a 2D matrix where each line corresponds to a frame number (or time value) and the columns contain the intensities I(q) and their associated SDs at the various scattering angles q. It is then a simple operation to generate another matrix where the lines correspond to the q-values and each column contains the intensities I(t) (and their associated SDs) corresponding to each frame number (or time value). A new data set consisting of I(t) vs. t "chromatograms" for each q-value can then be generated.
In the image above, the original I(q) vs. q data shown in the first image of this Help section have been transformed to I(t) vs. t data by pressing the Make I(t) button after selecting all files. The I(t) vs. t data are automatically displayed after the conversion, and the q values are now part of the resulting filenames. Since the On Make I(t), discard I(t) with no signal above st. dev. multiplied by "2.5" was selected in the Options menu (see here), the following Warning message appeared:
In addition, a test is automatically performed to identify regions within a sliding window (of 25 frames in this case) where the sum of the intensity is less than the negative of the sum of the corresponding SD values over the window. Regions with negative values could cause problems with the integral baseline subtraction procedure (see more below). This test identified just a single I(t) vs. t chromatogram failing it, as shown in a pop-up window:
Some cropping operations (see below) can be also performed to remove very noisy low-q datasets, such as the first three q values displayed in the Figure above (magenta, olive and greenblue) and/or to truncate the datasets if necessary. All operations are recorded in the bottom left panel.
The file names of produced data are shown in the Produced Data panel to the centre-left, and can be selected and saved to files using the appropriate buttons below it.
Select all will select all files in this panel.
Invert will allow toggling the selection between selected files and everything else not currently selected.
Similar will search for similar file names after selecting a single file in this panel.
Remove will discard the selected files.
Two types of files can be produced, csv-style (Save CSV) or regular 3-columns .dat files (Save).
Show will add the selected file(s) among those produced to the ones already displayed in the graphics window.
Show only will show only the selected file(s) among those produced in the graphics window.
In the Messages area, the operations performed are tracked, and computed parameters are shown. The display can be copied or cleared from the File pull-down menu.
The last line of the left-side panels contains the Help and Options buttons. On pressing the latter, a pop-up panel will be shown:
See here for a description of this module.
Below the US-SOMO HPLC-SAXS module graphics panel there are a series of buttons for performing several operations on the files displayed, some of which will become available only when multiple files are selected, or a region of the graph is zoomed, while others will become available only when single files are selected:
When a part of the graph is selected using the mouse/left button, the buttons in the bottom line become all available (only Crop Zeros and Crop Common are available when files are just displayed after selection).
To help the user decide if a baseline correction is needed, and to find a proper region of SAXS steady state signal at the end of the chromatograms, the currently implemented Integral Baseline method requires an analysis on blank frames. These "Blanks" (no less than 10 frames, possibly at least 20 or more must be available) should have been collected well before the void volume, and should preferentially be the same ones that were then averaged and subtracted from all the data collected during the chromatogram development.
After Blanks files have been loaded using the Add files button (see above), their analysis is launched by pressing the Blanks analysis button. The module will automatically convert the I(q) vs. q frames into I(t) vs. t chromatograms:
The two vertical magenta lines and their corresponding fields at the bottom of the buttons' zone define the beginning and end regions for the Blanks analysis. By clicking on one of the fields and then moving the mouse on the grey-scale bar-wheel just below the graphics window, these limits can be changed. This can also be done in steps of a single frame by clicking on the "<" and ">" buttons placed at the extremities of the bar-wheel. Alternatively, the limits can be manually changed by entering a numerical value in their respective fields.
The Blanks analysis is performed by clicking on the CorMap Analysis button. This will launch a pairwise Correlation Map analysis (see here for a descrption of the CorMap implementation in the US-SOMO HPLC-SAXS module). Before the analysis is effectively launched, a pop-up panel will appear:
It was found during the implementation of the Blanks analysis that finely spaced q values might result in cross-correlation effects in the CorMap analysis (see also here). Therefore, this pop-up panel will allow to chose a sampling in q space to eliminate or at least alleviate this problem. Since usually a one-every-two values sampling is sufficent, this can be directly done by pressing the Sample alternate q points button. Larger sampling intervals can be chosen by entering an integer value after pressing the Specify a larger gap in q points button. If no sampling is wanted, the Continue button should be pressed.
A second pop-up option will also allow to start the CorMap analysis above a chosen qmin value, to avoid including very noisy, low-q values in the analysis:
After these choices are made, the analysis is effectively launched, and the results are shown in a new pop-up panel (see here for a full description of the CorMap implementation):
The pop-up panel begings by reporting on the top bar the type of analysis (here "Blanks mode t 1 - 89"), the max q limit used (here 0.05 Å-1), and the sampling used (here "Only every 2nd q value selected").
Three plots are present on the top of the panel:
At the end of the text area, a checkbox is present. If selected, the paiwise analyses will be adjusted for multiple testing using the Holm-Bonferroni approach (Holm, S. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6:65-70, 1979; see here):
Note that in this case the Holm-Bonferroni multiple testing adjustment on a dataset where a one-every-two q-values sampling was applied has produced a completely green pairwise P-values map. Without sampling, this is what is obtained without the Holm-Bonferroni adjustment:
and with Holm-Bonferroni adjustment:
All data listed in the CorMap analyis pop-up window can be saved in a csv-type file with the Save button. Previously analyzed datasets can be recalled with the Load button.
After closing the CorMap analysis window, the Blanks data can be accepted by pressing the Keep button. Cancel will instead discard the current CorMap analysis.
The Integral Baseline analysis of the actual sample frames can then begin. Contrary to what was required in our previously developed Integral Baseline method, the current version requires that all I(t) vs. t chromatograms must be selected before hitting the Baseline button.
In any case, on pressing Baseline a first pop-up warning message will always appear:
This allows the user to proceed without using a Blanks reference set to judge if a stable baseline has been reached at the end of the chromatograms. In this case, only the Holm-Bonferroni adjusted pairwise comparison will be used.
If Blanks are to be used, a second pop-up warning message will appear:
alerting that a blanks analysis is needed to proceed any further, and offering up to three options:
After pressing OK, the graphics window will present all the selected I(t) vs. t chromatograms and switch to the Baseline mode of analysis:
As shown in the image above, this superimposes to the selected chromatograms three vertical lines on the right side, the last two lines of buttons under the graphics window are replaced by three colored fields (magenta-red-magenta), and a dashed line is drawn horizontally (orange). In addition, a Fix window width checkbox with its associated magenta-colored field in now present (default: 20 frames, unchecked), as well as a new Find best region button.
The first vertical magenta line, which by default is positioned at 75% of the available frames, has multiple usages:
The vertical red line defines the end for the sliding window analysis (default position: 5 frames from the end of the available frames).
The horizontal orange line represents the average intensity across the current window of the lowest q-value among the selected I(t) vs. t chromatograms.
It is important to remind that the baseline is set to be at zero at the beginning of the data on the left side.
The positions of the three vertical lines are indicated in the three background color-coded fields. By cliking on one of the fields, the corresponding vertical line position can be changed using either the grey-shades bar-wheel, or the "<" and ">" buttons at its sides. Manual values can be also entered.
If the Fix window width checkbox is not selected, moving either of the two vertical magenta lines will also change the width of the sliding window.
It is then best to first define a window width by moving either one of the vertical magenta lines, and then fix it by selecting the Fix window width checkbox. At this point, the entire window can by positioned by using either of the two vertical magenta lines. It is suggested to position it in a region where there is still some visible intensity decay, as shown below:
The baseline analysis is then completed by pressing the Find best region button.
This will launch a special CorMap analysis in which first a global CorMap calculation will be carried out between the entire range of frames from the first vertical magenta line to the vertical red line. Subsets of this CorMap analysis corresponding to the sliding window regions will then be extracted and compared with the average of all possible CorMap analysis results extracted from the pre-analyzed Blanks data for a sliding window of the same size.
In addition, the analysis will calculate the integrated average intensity at each frame of all the I(q) values from the minimum q-value selected up to the qmax defined in the Options panel (default: 0.05 Å-1).
The results will appear in two pop-up panels. The first one is analogous to the one appearing after the Blanks analysis:
Here, it can be appreciated the almost completely red left and top sides of the Pairwise P value map plot, originating from the fact that regions on the descending side of the elution peak were included in the analysis. This also heavily affects the right-side Red cluster size histogram, with an almost invisible huge size (≈5000) but extremely low count cluster greatly compressing the scale. If we zoom on the low red cluster size region, this is what becomes visible:
But most relevant is the second pop-up panel that will appear on top of the first:
The graph in this panel is composed of two plots, both as a function of the starting window position. The bottom histogram (left-side y-axis scale) reports the average red cluster size for each window in the sliding window ensemble. The horizontal green solid line defines the Blanks average red cluster size for all possible windows of the same size as the sliding window utilized for the Sample analysis (the dotted line represents + 1 SD). The bars in the histograms are colored red when they are above the Blanks + 1 SD value, while cyan and white when they are ≤ the Blanks + 1 SD value, with the white being the lowest value(s) (equal values are possible).
The top plot (right-side y-axis scale) reports the averaged I(q) for q ≤ the qmax value (0.05 Å-1 by default, as set in the Options), as the solid orange line, with the dotted orange lines representing ±1 SD. The solid magenta line defines the zero value expected for blanks-subtracted data when only buffer is present.
The goal of this combined analysis is twofold:
If the averaged integrated intensity -1 SD reaches at some point the zero line, then no Baseline correction is likely necessary.
If the averaged integrated intensity -1 SD at some point crosses and goes +1 SD below the zero line, then other issues might be present, such as incorrect Blanks subtraction, or drifting problems. In the latter case, a Linear Baseline correction might be indicated (see here).
If the averaged integrated intensity is always above +1 SD of the zero line, then an Integral Baseline correction could be necessary. The second condition warranting it is that there is an end region where a sufficient number of Sample frames (equal to the sliding window size by definition) is judged by the average red cluster size of the Pairwise P value Map to be similar within +1 SD of the average Blanks frames. Those are the starting frames listed in the first block of summary information, but beware of the presence of a single yellow-colored starting frame: it means that no frames passed the stringent Pairwise P value Map average red cluster size test, and that the listed frame is only the one having the lowest average red cluster size (which can be much higher than the Blanks average red cluster size). The user could try repeating the analysis using a different (smaller) sliding window size. Check also the starting/ending positions to be sure to include an appropriate end region for this analysis.
When both the Integral Baseline applicability conditions are met, the user could automatically transfer the position of the window into the Baseline module, by clicking on the Set region in the HPLC window bar at the bottom of the an analysis window. This will open a pop-up panel:
listing all possible starting positions for the baseline window, beginning with the farthest one. The user should pick a position matching with the lowest average integrated intensity frame position (orange colored text). If more than a lowest average integrated intensity frame is available, it is advisable to pick an earlier one, to avoid a potential undercorrection when integral baseline subtraction is performed. Once a position is chosen, clicking on OK will transfer it to the Baseline module panel:
To verify what the Integral Baseline will effectively produce, Test Baseline should be launched. This will show in scroll mode every original I(t) vs. t chromatogram, a smoothed version using a Gaussian smoothing kernel of 2n+1 points (where n is set in the Options panel, with n = 3 as default), the iterations in the Integral Baseline computation (whose number is also set in the Options panel, with 5 as default), and the final, integral baseline-corrected chromatogram:
In the example shown above, blue is an original I(t) vs. t chromatogram at q = 0.00791 Å-1, white its smoothed version with the default settings, cream, olive green, orange and pale yellow are integral baseline iterations 1, 2, 3 and 5, respectively (the 4th iteration is not visible, completely superimposed by the 5th), and light green is the final, integral baseline-corrected I(t) vs. t chromatogram. The Gaussian smoothing is applied to remove large oscillations in the original I(t) vs. t chromatogram, giving rise occasionally to values below the current integral baseline iteration, leading then to addition rather than subtraction in the computations. The final integral baseline is then subtracted from the original I(t) vs. t chromatogram, not the smoothed one.
As can be seen in the example above, the procedure appears to have produced a reasonable correction. All I(t) vs. t chromatograms can be checked in the Test baseline mode, which can be abandoned by pressing Cancel.
The Integral Baseline procedure can now be applied to all selected I(t) vs. t chromatograms by pressing Baseline apply. If files that failed the negative regions test within a sliding window (of 25 frames in this case) where the sum of the intensity is less than the negative of the sum of the corresponding SD values over the window are present, this message will again appear:
After pressing Ok, all the integral baselines will be computed and then subtracted from the I(t) vs. t chromatograms. When the overall computed change in baseline is found to be negative, no baseline correction is applied. A pop-up panel will alert the user listing the first 20 such occurences and giving the number of all the others found:
Each resulting baseline-subtracted chromatogram will have a "-bi" added after the q value and an "-s" at the end of the filename to indicate that an integral baseline subtraction was applied (if a linear baseline option is used, the first label will be "-bl"). The numerical value of the overall change in baseline and the alpha value (for an explanation alpha see here) are also added to the filename of the produced files, as shown in the Data files panel. Files where no baseline was subtracted will have a "0s" at the end of the filename:
First, the "sampling" pop-ups will appear, since in this case the sampling is not set by what was used for the Blanks:
In the following example, no sampling was applied. The sliding window size and the beginning-end of the baseline analysis region are set as with the procedure with Blanks (see above), and the Find best region button is then pressed. The CorMap results will this time be displayed with the Holm-Bonferroni checkbox automatically selected:
The second pop-up will also appear:
In respect with the analysis including a comparison with the Blanks (see above), there are two differences:
The fact that the right-hand sides of the peaks are nicely superimposed after baseline subtraction validates a posteriori the procedure used to build the baseline, since for a single species the elution peaks at different q-values should be strictly proportional to each other.
More checks of the Integral Baseline subtraction correctness can be performed using the Trial make I(q) mode. In this mode, the selected I(t) vs. t chromatograms are temporarily transposed back into I(q) vs. q frames and can be analyzed by either scaling or Guinier approximation utilities. In the example below, we have selected a subset of q-values from ≈0.008 to ≈0.21 Å-1, and we have pressed the Trial make I(q) button:
This will bring up again the gray-shades wheel-bar and change the two lowermost bars with the buttons below the graphics window. At the bottom, a Time range for I(q): label will appear, followed by two fields with red background indicating the region subjected to the Test I(q) procedure. The limits can be changed by either clicking on each red-colored field and then using the gray-shades bar-wheel at the top, or on the "<" and ">" buttons placed at its sides. Alternatively, if a region was pre-selected with the mouse, it can be applied by clicking on the Vis. range button. In this example, we have set the Time range for I(q) limits from frame 1100 to 1130.
Two operations can be then performed. Pressing the Scale Analysis button on the row above will change the layout in this way (note that, by pressing Log X and Log Y on the left-side commands panel, both axes have also been changed to log10):
The two lowermost rows now display the tools for scaling the back-generated temporary I(q) vs. q curves on top of each other. The two red-background fields now indicate the actual q range for scaling, which can be adjusted by clicking on each field and using the gray-shades bar-wheel at the top or on the "<" and ">" buttons placed at its sides; two vertical red lines will mark the corresponding positions on the graph. The Reset q range button will re-expand the q range.
The last row contains the scaling settings/commands:
In the image below, the scaling has been performed on the indicated q range. The Messages panel reports the statistics of the scaling process as applied to each curve scaled on the one with the lowest intensity:
By pressing Residuals, the residuals of the scaling operation are also shown. If the Scroll checkbox is selected, the scaled files can be examined one at a time, scrolling through them using the gray-shades wheel-bar or the "<" and ">" buttons placed at its sides. The file name of the data currently shown will appear below the gray-shades wheel-bar, as shown here:
A CorMap analysis can be also performed on the scaled set by pressing CorMap Analysis. This will produce two pop-up outputs, one containg the CorMap analysis on the full q-range available:
and the other limited to the qmax value presente in the Options (0.05 Å-1 in this case):
Note that one-every-other q-value has been utilized in this analysis. As can be seen, both the pairwise P-value map and the red pair % histogram indicate that with the exception of three frames of the ensemble (#2, #9 and #31, corresponding to frames #1101, #1108 and #1130), most are similar to all the others, with an overall ≈8-9% of red pairs. Limiting the lower q-values to 0.015 Å-1 reduced this overall % red pairs count to 6% (not shown), with frames #1101 and #1130 still being substantially different from all others.
If the Holm-Bonferroni adjusted P values checkbox is selected, these will be the results:
Clearly, the combination of the one-every-other q-value sampling and the Holm-Bonferroni adjustment is over-permissive for this dataset. If the analysis is repeated without the sampling, these are the results:
In this case, similar results are obtained as with the one-every-other q-value sampling and no Holm-Bonferroni adjustment.
Pressing Cancel will completely exit from the Test I(q) mode.
Pressing Trial make I(q) will instead exit from the scaling mode only.
Pressing then the Guinier button will call the other test function available in the Test I(q) mode:
If the maximum q value for the currently examined I(q) vs. q dataset does not reach the MW[RT] qmax cut-off value present in the Options panel for the Rambo and Tainer approximate molecular weight calculation method (see here), a warning will appear:
Pressing Ok will allow to proceed, showing the Guinier mode of the Trial make I(q) panel (in the case examined, the pop-up alert dit not appear, as the qmax utilized was >0.2 Å-1):
The lowermost row now carries the tools necessary to perform a Guinier analysis on the back-generated temporary I(q) vs. q curves:
The residuals of each linear regression can be seen by pressing Residuals:
Note how the average Rg recovered for this extended set, 14.8±0.2 Å, compares well with the 15.0 Å that can be calculated from the lysozyme average NMR structure (1E8L.pdb) using the WAXSiS server (http://waxsis.uni-goettingen.de/).
As with the scaling option, every individual Guinier plot can be visualized by selecting the Scroll checkbox and using the gray-shades wheel-bar:
At this point, a plot of the Rg values across the chromatogram together with a typical I(t) profile (continuous green curve) can be shown by pressing Rg plot:
A new row will appear below the graphics window, with these fields:
The scroll capability can also be activated in this mode, and the currently selected Guinier plot will be highlighted in the Rg plot:
Likewise, plots of the approximate molecular weight calculations can be shown by pressing the Approx. MW plot button:
Pressing Test I(q) button will bring back the main options of this utility.
Pressing the Cancel button will exit the Test I(q) utility.
If Gaussian analysis is not required, a series of I(q) vs. q frames can be re-created at this stage from the baseline-corrected data by pressing the Make I(q) button.
Upon selecting a single I(t) vs t chromatogram, the actual SD associated with it can be visualized by selecting the Err checkbox in the Data files commands section, as shown in the image below:
By pressing the SD eval. button, two vertical red lines will be superimposed on the initial region of the chromatogram, and two red-background fields controlling their position will appear in the bottom row of the commands below the graphics window:
An additional checkbox, 2 regions, if selected will duplicate the vertical lines and their associate fields (colored magenta this time), allowing to utilize more than one flat region for the SD estimation:
The SD evaluation is carried out by fitting the data included between each zone with a 3rd degree polynomial, and taking the RMSD of the fit as the SD. If two regions are chosen, the final SD will be an average between the values computed from each region.
After adjusting the zone(s) for the SD evaluation, pressing Keep will accept the values, and the SD apply button becomes available. Pressing it will apply the SD calculation to any selected chromatogram. In the example below, the same chromatogram is plotted twice, with the old (salmon) and new (slate gray) SDs:
A blow-up of the main peak region highlights how the two SDs are very close to each other, demonstrating that the assumptions taken for this alternative SD evaluation produce SDs which are very similar to the ones that have been associated to the original SAXS data using a Poisson distribution. The main difference is that the original SDs vary slightly with the intensity for each I(t) vs. t chromatogram, while the baseline fluctuations method produces constant SD values for each I(t) vs. t chromatogram.
Gaussian decomposition of not baseline-resolved peaks is another utility present in the US-SOMO HPLC-SAXS module. Decomposition with symmetrical Gaussian functions will be first described using a bovine serum albumin (BSA) SEC-SAXS run using two 7.8 × 300 mm ID columns packed with hydroxylated polymethacrylate particles (TSK G4000PWXL, 10 µm size, 500 Å pore size, and G3000PWXL, 6 µm size, 200 Å pore size, Tosoh Bioscience, Tokyo, Japan) connected in series, protected by a 6 × 40 mm guard column filled with G3000PW resin (Tosoh). The data presented capillary fouling evidence, and were thus subjected to Integral Baseline correction (not shown).
Before proceeding to Gaussian analysis (whose theory can be seen here), a SVD analysis could be useful. In SVD analysis, the number of significant singular values in the decomposition should be equal to the number of components in the data, and thus to the minimum number of Gaussians required to accurately reconstruct the data (see here).
The baseline-subtracted data can be subjected to Gaussian analysis by first selecting a single chromatogram, and then pressing the Gaussians button. By default, the US-SOMO HPLC-SAXS module will consider symmetrical Gaussians, but distorted Gaussian functions are also availble and can be selected from the Options menu (see here). The choice must be done before starting the following procedure. An example of a data processing with non-symmetrical Gaussians is presented here.
On pressing Gaussians, two new rows will appear at the bottom of the graphics window. If a previously-generated set of Gaussians was present or loaded from file, the Gaussians will show up under the peak(s) together with vertical lines indicating their centers.
Clear will remove currently-generated Gausssian, and allow to start a new analysis. If Gaussians had been loaded from file, the Clear cached Gaussian values button in the Options menu should be used.
Each time the New button is pressed, a new Gaussian will be added (green colour), with pre-set center, width and amplitude shown in the three rightmost fields (additional fields will be present if distorted Gaussians functions are used; see here). By clicking on each field, and then using the gray-shades bar-wheel, each Gaussian can be adjusted to initialize the process (usually, only the centers need to be positioned under the peaks). If the Match checkbox is selected, the height of each Gaussian will be automatically adjusted so to match the height of the experimental I(t) vs. t curve at the Gaussian current position.
Del will remove only the current Gaussian.
Clicking on the "<" and ">" buttons will toggle among the Gaussian present, whose identifying number is shown in the field between them. The active Gaussian is identified by a magenta vertical line positioned at its center, while blue lines are used for the others. The limits for the analysis of the chromatogram are shown with two vertical red bars, whose position is shown in the two red-background fields in the bottom row, before the To produced data button.
The SD checkbox controls whether the data associated std. dev. values will be used in the fitting procedure (default: not selected). It is recommended to select this checkbox only after a first round of fitting with the various algorithms provided has been performed, as the SD can only be used with the LM algorithm at the time of writing this Help section (April 2016).
Once the initialization is completed, pressing the Fit button will bring up a window controlling the fit procedure, shown below:
See here for a description of the Fit module.
In the first cycle of iterations, it is best to keep the original centers fixed:
In the example shown, a not well-defined aggregates peak is present at the beginning, and an extended initial baseline is not present. If the first Gaussian is left free to adjust, it will expand too much to compensate for the missing initial baseline. Therefore, in such situations it is best to keep fixed the position of the first Gaussian:
A final round of fitting can then be performed using the SD and allowing a 5% variation on the Gaussian centers at each iteration, until a satisfactory fit of the main peak(s) is obtained:
If some datasets have missing or NaN values for one or more SD values, a pop-up menu will appear listing all the files presenting this problem, and with how many occurrences. The user can then select between three options: drop the datasets containing these non-defined SDs; drop just the frame (or time) point missing the SD(s); or not use SD weighting.
The global improvement of the fit can be also judged by the rmsd (SD checkbox not selected) or χ2 (SD checkbox selected) value which is updated next to the Fit button. The residuals of the fit can be visualized by pressing the Residuals button, which will split the graphics window in two, and show a plot of the fit residuals below the main plot. The residuals plot can be removed by pressing Residuals again (see more below). In the example shown above, the residuals are weighted by the std. dev. associated with the experimental points (SD checkbox selected; a By percent residuals option is also available).
Once a satisfactory fit is reached, pressing Keep will accept the current Gaussians for further work. But to save the parameters of the current Gaussians in a file, the Save button has to be pressed before Keep.
Cancel will cancel the operations and remove all the Gaussians.
Once an initial set of fitted Gaussians has been produced, it should be globally fitted to all chromatograms. However, performing this operation directly on all chromatograms can be very computationally intensive. For this reason, it is best to perform it on a subset of all chromatograms, and the global fit results are then propagated to all remaining chromatograms. Importantly, in the global fitting procedure the centers and widths of each particular Gaussian are optimized so to be the same across all chromatograms, and only the amplitudes are then fitted.
To select a subset of data, the Select button is pressed, which will open the pop-up selection panel (see image below and here).
It is advisable to perform the global fitting avoiding the very first few low-q, very noisy, and the last high-q, very low signal I(t) vs. t chromatograms. In the example we are illustrating, we start from chromatogram # 8 (q = 0.007813 Å-1) and select every 4 chromatograms up to # 454 (q = 0.12020 Å-1). The I(t) vs. t chromatogram on which the initial set of Gaussians was optimized is also included (Select Additionally button). Pressing Transfer selection to main window will close the pop-up window and the selected files will be shown in the main HPLC-SAXS module graphics window:
The Global Gaussians button is now available. Pressing it will simply find the amplitudes best fitting all the selected chromatograms based on the centres and widths found on the initial chromatogram. This operation has to be performed before the global fit.
If datasets having points with missing or NaN std. dev. values are found, a pop-up panel will appear:
When just a few problematic points are found for each file, the Drop points with 0 SDs option can be safely used. The global Gaussians operation will then be completed:
In the image above, the Global Gaussians results on the Nth selected files are shown, together with the grouped fit residuals. The common centers and widhts, not optimized but just based on the initial chromatogram fit, are displayed in the graph as vertical and horizontal bars, respectively. Note that the Residuals plot x-axis scale was manually optimized (right-click on the scale) to make it comply with the fit limits in the top panel.
Save will save the resulting Gaussians to the current selected directory, with extension -gauss.dat for symmetrical Gaussians of single files and -mgauss.dat for Gaussians of multiple files. For distorted Gaussians, the extensions will be -mgmg.dat, -memg.dat, and -memggmg.dat for the GMG, EMG and EMG+GMG Gaussians, respectively.
Global fit, which becomes available instead of the Fit button once a series of chromatogram is selected and after at least an initial set of Gaussians is generated/loaded, can now be used to optimize all the centres and widths of each Gaussian along all the chromatograms to common values for each family of Gaussians. The operation is controlled by the same pop-up Fit panel as for the single chromatogram case (see here), but only the LM method is currently (April 2016) available. In this example, it is best to first perform a global fit round keeping the Gaussians 1, 2 and 4 fixed, and then perform a second round leaving all parameters free.
In the image above, the results of the Global fit are shown together with the grouped fit residuals. Furthermore, a new set of tools is available to judge the goodness of the fit.
In the Global fit by q graph it is possible to visualize either one of or both the two plots, by selecting/deselecting their respective checkboxes positioned just below it (Plot Chi^2/RMSD and Plot CorMap P values). Note that in the image above, where both plots are shown, their respective y-axis scales have been manually modified to allow a better visualization of each plot. The dashed green and yellow horizontal lines mark the usual cut-off P-values (P ≥ 0.05, above the green line; 0.05 > P > 0.01 between the green and yellow lines; P < 0.01, below the yellow line).
Note that the limits of the fit have been moved to exclude the first peak and the tail of the main peak. This was done to concentrate the goodness-of-fit indicators toward the most important part of the fit, including the top (2/3)rds of peaks 2, 3 and 4 (each time the limits are moved, the normalized χ2 and P-values are recomputed by pressing the Recompute nChi^2 button). With these limits, the normalized χ2 values display "reasonable" values, ≈1.5 for the lowest q angles (up to q ≈0.035 Å-1), then almost linearly decaying to ≈0.5 for q ≈0.8 Å-1, being stable afterwards, for a global χ2 ≈0.95. Likewise, the CorMap P-values show a slight trend toward better values as the q increases, but the distribution of really "bad" P-values appears to be substantially random.
The correlation between the goodness-of-fit indicators and the distribution of the residuals can be examined for each original/fit I(t vs. t pair by selecting the Scroll checkbox:
In the image above, only the CorMap P-value are shown. The current chromatograms pair is highlighted in the CorMap P-values plot by an enlarged symbol (orange square in this case). Scrolling is performed by either using the grey-scale bar-wheel, or by clicking on the the "<" and ">" buttons placed at its sides. By selecting/deselecting the three checkboxes next to the Scroll checkbox (P >= 0.05, 0.05 > P >= 0.01, P < 0.01), only the subset(s) whose P-values are within those of the selected chechbox(es) will by scrolled.
In the example shown above, by examining the residuals' plot it is clear that the "bad" P-value it is due to a poor fit in the inflection point betweern the 3rd and 4th peaks. If we examine a chromatograms pair just two q values above the first one examined in detail, we can see that oscillations in this zone produce an excellent P-value, although this still appears to be a difficult zone to fit with symmetric Gaussians:
The noticeable worse fitting and the end of the main peak could indicate either a slight non-pure Gaussian shape of the peak, or the presence of a small amount of some trailing material in this region.
It is best to first Save and then Keep the results, and then select all the available I(t) vs. t chromatograms (use Select all if only I(t) vs. t data are present in the Data files section).
Global Gaussians can now be applied to all the selected chromatograms. Again, if datasets having points with missing or NaN std. dev. values are found, a pop-up panel will appear (not shown).
The image above shows the global Gaussians results after applying the global fit parameters found on a subset of data to all chromatograms. Note that in the series of graphs above, the residuals x-axis was rescaled (using the graph controls accessed by right-clicking on the graphics window plots) to align it with the selected fit region delimited by the two red vertical lines.
Save and Keep can then be sequentially pressed to store and accept the global Gaussian results.
Pressing the 3D button will generate a 3D plot of the data, allowing easier detection of potential fitting issues. First a pop-up window will appear:
More infos about this small module can be found here.
This interactive plot can show any selected set of the Global Gaussians over any collection of curves. The interface is fully interactive for rotations, scaling and zooming along with multiple display and save controls. Its utilization is helpful for visualizing the quality of the global fit.
After Gaussian decomposition, the Trial make I(q) procedure can be repeated. First, all the available I(t) vs. t chromatograms for which Gaussians have been produced are selected, and the Trial make I(q) button is pressed. The third commands row under the graphics window will now show additional options:
The round checkboxes labeled none, 1, 2, 3, and 4 allow selecting which Gaussian will be used to produce the corresponding decomposed I(q) vs. q data, as a pointwise % of the original I(t) vs. t data based on the relative contribution of all Gaussians at that particular point in t space. If the square as pure Gaussian checkbox is selected, the actual Gaussian value will insted be used (effectively smoothing the data).
In the first example shown below, the Rg plot for the region of the main peak using the 4th Gaussian can be seen:
The contribution of the 3rd Gaussian under the main peak can be now evaluated:
As can be seen, there is a slight contribution (see the ~500-fold reduction in intensity in the Guinier plot) from the peak preceeding the main peak, evidenced by the fairly constant but considerably higher Rg values (≈ 44.5 Å), likely identifying this material as a BSA dimer (also confirmed by the average MW[RT] value).
If we perform this analysis selecting the top region of the dimer peak (frames 72-90), we find similar Rg values, ≈ 43.7 Å, almost evenly distributed across the peak:
Note that some of the curves present an upward curvature at low q-values, likely indicating a non-ideal baseline correction for this sample.
Finally, the contribution of the 2nd Gaussian under the trimer peak is evaluated:
finding higher Rg values (≈ 60 Å) and a reasonably flat distribution.
The Scroll feature is also available, allowing the examination of the individual Guinier plots. Likewise, the Approx. MW plot can show the approximate molecular weight values calculated with the Rambo and Tainer method (Accurate assessment of mass, models and resolution by small-angle scattering. Nature 496:477-481, 2013) . However, as it requires to produce meaningful results a more extended q range than that available for the HPLC-SAXS BSA study presented here, we will not present such plots here.
To allow the visualization of the Gaussians, the To produced data button is provided which produces curves of individual Gaussians and their sum. This is available in either Gaussian or Global Gaussian modes. The resulting curves are collections of data points that can be visualized outside of the Gaussian modes. The Global Fit method requires a simultaneous fit of all the selected curves. This is internally represented by joining all the selected curves along the time/frame dimension to produce one long curve. Of course, each curve is generally on the same time/frame axis range, so to maintain increasing time/frame numbers, curves subsequent to the first one are placed into the joined curve with an offset in time/frame.
To visualize the joined curve and the Global Gaussian fit to the joined curve the Make result curves button is provided. This will create the joined curve along with the joined Global Gaussian fit as a pair of curves that can be visualized outside of the Global Gaussian mode, as in the example shown below:
the first operation is to rescale it to one of the high intensity but relatively low-noise I(t) vs. t chromatograms. This is done by selecting the two files:
and pressing Repeak in the left-side command panel, which will bring up a small window asking to identify the target chromatogram (in case multiple were selected).
Usually concentration detector data have no associated SDs. In this case, another pop-up panel will appear presenting three options:
The repeak operation is then automatically performed, and another pop-up message will appear:
If no time-shift between the concentration and the SAXS detectors is present, the repeaked concentration file can then be directly associated with the SAXS datasets. Otherwise, it is better to perform first the timeshift operation (see below) before setting the concentration file. The result of a re-peak operation is shown below, and the scaling factor is added to the concentration dataset filename.
After re-peaking, the concentration chromatogram usually must be time-shifted to align its peaks to the I(t) vs. t chromatograms using the Timeshift button.
Again, at least two files must be selected, one is the concentration data, the other belonging to the I(t) vs. t (the file used for re-peaking is normally used for this operation). An automatic alignment is first performed, using the highest intensity peaks. The alignment can then be refined manually by left-clicking and moving the mouse over the grey-shades wheel bar below the graphics window until the two chromatograms are best aligned.
The value of the timeshift is reported in the field next to the grey-shades wheel bar.
Cancel will stop the operation.
Keep will keep the time-shifted data. The produced data will have the timeshift value added to its filename on saving.
Another pop-up panel will appear, asking to associated the time-shifted concentration file to the SAXS data:
Answering "yes" will then associate the re-peaked, time-shifted concentration data to the I(t) vs. t SAXS dataset under analysis. This operation can be anyway performed at any time by selecting only a concentration chromatogram dataset, and pressing Set. The concentration chromatogram shown in this example is then cropped to have approximately the same frame number as the SAXS I(t) vs. t chromatograms.
The re-peaked, time-shifted concentration chromatogram can be now fitted with Gaussians, using for initialization the set derived from the I(t) vs. t chromatograms (note: it is mandatory that the same number of Gaussians be used for both the concentration and I(t) vs. t chromatograms).
This is done by first selecting only the concentration chromatogram and then pressing Gaussian, which will bring up the current Gaussian parameters automatically rescaled to the highest intensity in the concentration chromatogram:
Pressing Fit will then bring up the Fit window (see here) and an initial round is done by keeping fixed both the position and widths. If necessary, a refinement can be done by keeping fixed the smallest, front eluting peak(s), and allowing only a limited shift to a % of the initial values from the widths and positions determined from the SAXS data (suggested: 2-3% max). This should compensate for slight misalignment between the concentration and SAXS detectors chromatograms.
As evidenced in the image above, some band broadening has occurred between the UV-VIS and SAXS detectors. While the issue appears to be relatively minor here, it can be more serious. To at least partially mitigate this issue, we have implemented a re-shaping routine that re-aligns the shape of the concentration detector chromatogram to that of the SAXS detector chromatograms. It is based on determining first the area under each Gaussian peak in the concentration chromatogram after fitting it with the SAXS-derived Gaussians with minimal centers and widths changes, as described above. Then, when the Make I(q) routine is launched, the concentration chromatogram Gaussians can be optionally re-shaped on the SAXS-optimized Gaussians, keeping their areas fixed and adjusting the other parameters (see below).
The Save and Keep buttons must be then pressed to store and associate the resulting Gaussians to the concentration chromatogram. On re-generating the I(q) vs. q frames (see below), each concentration Gaussian peak will be mapped onto the corresponding I(t) vs. t peaks.
The Make I(q) button becomes available every time that more than one I(t) chromatogram is selected. If Gaussian fitting was performed, pressing it will produce a series of I(q) vs. q curves for each Gaussian peak for each frame of the chromatogram on which the global operations have been carried out. An option panel in a pop-up window will allow several choices:
A description of this module can be found here.
Once the I(q) vs. q files have been generated, it is possible to view the resulting Gaussian contributions and their sum, as shown below:
Here the original and decomposed I(q) for frame #59 (cream), originally presenting an overlap between the trimers and dimers peaks, are shown, together with the reconstructed sum with baseline back-addition (see the legend for details). The drop of intensity at q values > 0.07 Å-1 for Gaussian peak #1 (purple) is due to its contribution vanishing in the high q range. Note how there is a contribution from Gaussians #1, #2 (orange), and #3 (olive green) in this frame (peak #4, not contributing at all in this frame, is not shown). Note also how the reconstructed curve with baseline back-addition (whose color would be cyan) perfectly superimposes with the original frame data (cream), and thus is almost not visible in this frame except at the very end of the q range.
A zoom into the low q region for frames #75-86 of the Gaussian peak #3 it is shown in the next two images, before and after concentration normalization (Normalize button):
In the latter, an average curve (obtained by pressing the Average button) is also superimposed. Such re-generated I(q) vs. q data can be directly exported in the main US-SOMO SAS module for further operations by pressing the To SOMO/SAS button.
If a concentration chromatogram is associated with the data, an additional utility present in this module allows to map a single selected I(q) vs. q dataset onto the concentration chromatogram, by pressing the Concentration reference button:
In the example shown above, the I(q) vs. q data for the decomposed peak #3 frame #80 are shown with their associated errors, and below it the position of this dataset is shown by the vertical red line on the associated concentration cromatogram. Each time a different chromatogram is selected, its position will be mapped on the concentration plot.
Pressing the Concentration reference button again will make this additional plot disappear.
Finally, the data shown in any of the plots currently visualized can be saved in csv-formatted files by pressing the Save plots button. This will open a pop-up dialogue window where the location and the root filename for the cvs files can be set.
This document is part of the UltraScan Software Documentation
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Last modified on July 11, 2016.