What is SAXS/SWAXS?
Hecus X-Ray Systems, founded in 1992, is traditionally specialized on innovative system solutions for X-Ray nanostructure analytics. The strong focus on small-angle X-ray methods - the Otto-Kratky heritage - serves a wide community of researchers and engineers, who need SAXS and related techniques as practical and reliable tools in their challenging laboratory practice, and who want to use the techniques routinely.
What is SAXS/SWAXS?
Small- and Wide-Angle X-ray Scattering (S/WAXS) are non-invasive analytical techniques to investigate the structure of non-crystalline or partly crystalline materials. Both the supra- or macromolecular domain as well as the interatomic distances in small molecules or crystals are investigated.
Fields of Application:
- Liquid Crystals
- Powders & Cream Formulations
- Coatings & Films
Small angle X-ray scattering of proteins – or of nanoparticles in general – in solution has proven to be a valuable method for their (nano)structural characterization and parameterization like size and shape. The most prominent parameter is the particle’s radius of gyration Rg, a value which relates to the size of the particle and which can be easily extracted from the inner part of a SAXS curve:
I(q) ~ I(0)*exp(-q2*Rg2/3) (1)
with I being the scattered intensity from the sample, q the reciprocal scattering vector (related to the scattering angle 2θ) and I (0) being the extrapolated intensity to the angle zero. The relation between q (reciprocal metric units, nm-1 or Å-1) and 2θ(°, angular units) is given by q = 4π (sinθ)/λ, with 2θ being the scattering angle with respect to the incident beam and λ the wavelength in nm or Å of the used X-ray beam.
A solutions of the protein prepared by dissolving the lyophilized powder of the protein bovine (serum) albumin (BSA from SIGMA chemicals, St.Louis, MO) in 10 mM PBS-buffer (pH = 8.0). The final concentration was 15 mg/ml (1.5%). Small-angle X-ray scattering (SAXS) measurements of this protein solution and the respective buffer was carried out with a HECUS S3-Micro SAXS camera attached a Xenocs microbeam delivery system (Cu-target, wavelength λ= 1.54 Å and FOX3D-optics), operating at a power of 50 W. The vertical entrance slit aperture was set to 200 µm resulting in a flux of 1.5*107 photons/s. The liquid samples were filled into quartz capillaries of 1 mm diameter and measured at 20°C for typically 2000 s. Before the measurements the relative primary beam intensity and the X-ray transmission of the samples was measured with a pin-diode. The SAXS-patterns were recorded with a linear 1D position sensitive detector (1024 pixels with 54 µm pixel-width) within a q-range up to 0.6 Å-1. The incident primary beam was blocked by a motorized adjustable beamstopper (2 mm W) located in front of the detector. Calibration of the q-scale (converting pixel values into q-values) was done with the powdered Ag-behenate which has a calibrated d-spacing of 58.38 A. Raw data processing of the scattering curves (background subtraction after normalizing) was done with the primary data evaluation program EasySWAXS (HECUS) and the processed data were subsequently analyzed with the program package ATSAS 2.3. (D. Svergun, EMBL, Hamburg).
In Fig.1 the inner part of the SAXS curves of BSA in buffer (I (q) s) and of the buffer (I (q) b) are shown. Relative primary beam intensity and exposure time were the same in both measurements therefore the background correction was simply done by subtraction and normalizing by their transmission Ts and Tb, respectively.
I(q) = I(q)s /Ts – I(q)b/Tb (2)
Generally, for diluted protein solutions the transmission of sample solution and buffer will be nearly the same, in this particular case Ts and Tb were 0.32.
Figure 1. SAXS-curves of BSA 1.5% in buffer (red), of the buffer (green) and of BSA-buffer (blue), zoomed into the inner part ( 0 < q < 0.2 Å-1).
Figure 2. Guinier-plot of the SAXS curve of BSA 1.5%. A value of 29.2 Å for Rg was obtained from the slope within the shown q-limits qmin and qmax of 0.018 < q < 0.05 Å-1, with Rg*qmax being 1.5.
Fig 2. shows the SAXS-curve of 1.5% BSA plotted in the the linearized form of equation 2, the so-called Guinierplot ln(I(q)) vs q2. The linear slope is directly proportional to Rg2, resulting in a Rg value of 29.2 ± 0.3 Å for the particle.
These background corrected SAXS data in reciprocal space have been fouriertransformed into real-space, applying the program GNOM 4.5 (ATSAS package). The only input parameter for this procedure are the qmin and qmax values of the SAXS-curve and the a-priori estimated Dmax value, a maximum size value up to which the real-space function is being calculated. The estimation of Dmax is connected with the available qmin value of the scattering curve by qmin < π/Dmax. As a result we obtain the real-space function the so-called p(r)-function or distance-distribution function (see Fig.3), which is characteristic for the particle’s shape, size and internal electron density homogeneity.
Figure 3. Distance distribution function of 1.5% BSA in solution obtained from the SAXS-curve in the q-range of 0.026 < q < 0.3 Å-1 using the program GNOM. The maximum particle size is approximately 100 Å (where the function approaches 0). A value of 29.3 ± 0.6 Å for Rg was obtained from the p(r)–function, which is basically the same as it was obtained independently from the Guinier-plot in reciprocal space.
A low resolution shape simulation from the SAXS-data was done applying the program DAMMIN (ATSAS 2.3 package). This program attempts to find a 3-dimensional shape by a certain algorithm by searching a shaped object whose theoretically calculated scattering curve fits the experimentally obtained one. No a-priori assumptions were made. Fig. 4 shows the result of one of such run. It has to be stressed that the obtained model is of low spatial resolution and is only one of many possible models which fits the experimental scattering curve in the experimentally limited q-range. The usual procedure now would be to perform many runs of shape simulations on the same experimental SAXS-curve because each run results in a slightly different model shape. An ‘averaged’ model can then be extracted by doing a spatial averaging over all calculated models.
Figure 4. Shape simulation of the BSA low-resolution structure from the SAXS-curve using the program DAMMIN (one run). The open circles (blue) are the experimental SAXS-data, the green line (coinciding with the red one, therefore not visible) is the fitted SAXS-curve obtained from GNOM and the red line represents the simulated SAXS-curve from the model shown in the right part of the figure.
An estimation of the protein’s size and shape can be quickly obtained with the S3-micro SAXS system using a protein solution of 1 – 2 %. However for a more accurate evaluation of these parameters lower concentrations are necessary. Usually this is done in a concentration series experiment by measuring SAXS-curves at different (and lower) protein concentrations and extrapolating the SAXScurves then to zero-concentration.
Source: Hecus X-Ray Systems
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