Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute
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Liu, L., Boldon, L., Urquhart, M., Wang, X. Small and Wide Angle X-Ray Scattering Studies of Biological Macromolecules in Solution. J. Vis. Exp. (71), e4160, doi:10.3791/4160 (2013).
In this paper, Small and Wide Angle X-ray Scattering (SWAXS) analysis of macromolecules is demonstrated through experimentation. SWAXS is a technique where X-rays are elastically scattered by an inhomogeneous sample in the nm-range at small angles (typically 0.1 - 5°) and wide angles (typically > 5°). This technique provides information about the shape, size, and distribution of macromolecules, characteristic distances of partially ordered materials, pore sizes, and surface-to-volume ratio. Small Angle X-ray Scattering (SAXS) is capable of delivering structural information of macromolecules between 1 and 200 nm, whereas Wide Angle X-ray Scattering (WAXS) can resolve even smaller Bragg spacing of samples between 0.33 nm and 0.49 nm based on the specific system setup and detector. The spacing is determined from Bragg's law and is dependent on the wavelength and incident angle.
In a SWAXS experiment, the materials can be solid or liquid and may contain solid, liquid or gaseous domains (so-called particles) of the same or another material in any combination. SWAXS applications are very broad and include colloids of all types: metals, composites, cement, oil, polymers, plastics, proteins, foods, and pharmaceuticals. For solid samples, the thickness is limited to approximately 5 mm.
Usage of a lab-based SWAXS instrument is detailed in this paper. With the available software (e.g., GNOM-ATSAS 2.3 package by D. Svergun EMBL-Hamburg and EasySWAXS software) for the SWAXS system, an experiment can be conducted to determine certain parameters of interest for the given sample. One example of a biological macromolecule experiment is the analysis of 2 wt% lysozyme in a water-based aqueous buffer which can be chosen and prepared through numerous methods. The preparation of the sample follows the guidelines below in the Preparation of the Sample section. Through SWAXS experimentation, important structural parameters of lysozyme, e.g. the radius of gyration, can be analyzed.
1. Preparation of the Sample
* Solid samples (including powder samples) can be directly placed in the sample holder (no capillary necessary), whereas liquid samples must be placed in a capillary.
Start-Up of the SWAXS Machine
2. Source Cold Startup Procedure
3. Chiller Procedure
NOTE: If at any time the error "E 01" shows up on the temperature display, follow the Chiller Shutdown instructions, refill the bath unit by pouring purified water into the tank fill, and then perform the chiller Startup procedure again.
4. Shutdown of Chiller
5. Turning on the Vacuum
6. Detector System Setup
8. Software Procedure
9. Source Shutdown Procedure
SAXS and WAXS altogether can provide structural information of the sample through the following parameters: the radius of gyration, particle size and shape, solution structure factor, specific inner surface and pore size, lattice type and dimension, and electron density 1. SAXS and WAXS can also be applied to the study of protein dynamics 2.
The structural information of SWAXS experiments is obtained by comparing the experimentally detected spectra and the computational results of the system. The computational results were calculated in the software with a reasonable effective potential V eff(r)developed from statistical mechanics models, such as the Ornstein-Zernike (OZ) integral equation theory (an example of such analysis may be seen from Ref. 3).
As part of the data analysis methods, models for the SWAXS absolute intensity I(q) will need to be developed in the software for study, where the scattering intensity, I(q), is a function of the momentum transfer in reciprocal space, the scattering vector q=4π sin(θ/2)/λ . q is a scalar quantity which is connected to the scattering angle, θ, and the wavelength of the radiation, λ. q lies in the range of 0.03 - 0.6 Å-1 in a typical SAXS experiment with a selected sample-to-detector distance. The size of the region investigated in real space is related to q by r=2π/q, and lies in the range 11-2000 Å 4. WAXS, on the other hand, can resolve spacing larger than 3.3 Å. I(q) depends on the atomic features and the position of the atomic scattering centers. In the SWAXS experiment, first the measured intensity vs. channel must be calibrated to intensity vs. q or spacing d (Figure 1 and Figure 2). Then the software may be utilized to analyze the structural information.
An example of the SAXS analysis of the lysozyme in 2 wt% water based aqueous buffer is shown in Figure 3. The value for radius of gyration obtained and shown in Figure 3 compares nicely to the expected value of approximately 1.44 nm 5. More examples of how to apply SAXS to biological macromolecules may be found from Refs. 6-13 . An example of the WAXS analysis of the liposome dispersed in aqueous solution is shown in Figure 4. The equally spaced peaks decreasing with increasing q, lends the liposome in the water based aqueous solution sample to a lamellar structure. With each lamellae, there is a decrease in the scattering that will occur.
Figure 1. The SAXS Calibration with ImageJ-macro software. The sample used is silver stearate with d spacing 48.68 Å. The primary beam is located at channel 367 and the five major peaks (or lattice parameters of the sample) are located at 539, 717, 896, 1075, and 1253 channels, respectively.
Figure 2. The WAXS-Callibration with the ImageJ-macro software. The sample used is Para-Bromo Benzoic Acid powder. The six major peaks (or lattice parameters of the sample) are located at 130, 484, 555, 613, 657, and 902 channels, respectively.
Figure 3. Background-subtracted SAXS raw-data of lysozyme (2 wt%). The Guinier-plot from EasySWAXS software can utilize the very low q part of the raw data to find the radius of gyration.
Figure 4. Background-subtracted WAXS raw-data of liposome dispersed in a water based aqueous solution is shown in Figure 4A. The schematic diagrams of the structure of liposome (1D lamellar), its hydrophilic head and hydrophobic tail, its phospholipid membrane stack, and its electron density function are shown in Figure 4B. Click here to view larger figure.
The comparative procedure of the SWAXS system allows for numerous variables to be determined from experimental analysis. The parameters that are attained from the analysis can be used for different purposes according to the sample and experimental setup. SAXS provides information about nano-scale size and shape of the object, whereas WAXS focuses on the atomic and micro-scale structure (e.g. molecular lattice, unit cell dimension symmetry). More specifically, for particles in dilute solutions, SAXS can study the radius of gyration, particle size, and shape; for high-density samples, SAXS may study the structure factor of the solution; for random porous/2 phase systems, SAXS can study specific inner surface and pore size; and for liquid crystalline samples, WAXS may study lattice dimensions and the unit cell structure. However, a limitation of SWAXS is that a wide range of distribution of particle sizes or polydispersity will severely downgrade the experimental results.
No conflicts of interest declared.
We would like to thank Dr. Manfred Kriechbaum of Hecus XRS and the Institute of Biophysics and Nanosystems Research at the Austrian Academy of Sciences in Graz, Austria. LL and XW were supported in part by U.S. Department of Energy, under NERI-C Award No. DE-FG07-07ID14889, and U.S. Nuclear Regulatory Commission, under Award No. NRC-38-08-950. The SWAXS instrument is also supported in part by U.S. Department of Energy, under Award No. DE-NE0000325.
|The System3 Small- and Wide-Angle X-Ray Scattering (SWAXS) Camera||Hecus XRS and IBN,
|GNOM||ATSAS 2.3 package by D. Svergun EMBL-Hamburg|