Small-Angle X-ray Scattering for Pharmaceutical Applications

The author describes the development of small-angle X-ray scattering and analyzes its advantages in the characterization of drug-delivery systems and large molecules. This article is part of a special Analytical Technology issue.
Oct 01, 2010
Volume 2010 Supplement, Issue 5

Small-angle X-ray scattering (SAXS) offers various ways to characterize drug-delivery systems and large molecules. Understanding the structure of drug-delivery systems and large molecules at a molecular level is a crucial step in designing drugs and drug-delivery systems alike.

The SAXS technique can provide insights into structures in the 1–100 nm range. SAXS requires little or no sample preparation and enables scientists to run experiments at or close to in vivo conditions.

Historical perspective

Röntgen discovered X-rays in 1895. In 1912, Laue discovered the diffraction of X-rays by crystals (1). Guinier's work in late 1939 led to the main principles of SAXS (2). In the 1940s and 1950s, Otto Kratky investigated X-ray diffraction at small angles as a technique for the structural analysis of macromolecules. He developed the SAXS method into a powerful tool for structural research, particularly in the field of polymers and molecular biology (3). Considered one of the fathers of SAXS, Kratky founded the Institute for Physical Chemistry in Graz, Austria, which became an early center for this technique. The institute led to many advances in SAXS such as the first commercial instrument for SAXS.

Early SAXS experiments took place in laboratories. In the 1970s, the availability of synchrotrons and high-intensity synchrotron radiation helped bring the technique to prominence. In recent years, technical advances have made laboratory-based SAXS instruments attractive again.

SAXS basics

Figure 1: Positive interference of two spherical waves from an electron pair can be seen (left) at larger angles if the electrons are close to each other (e.g., in a crystalline structure) and (right) at smaller angles if the distance is greater (e.g., in a macromolecule). (ALL IMAGES ARE COURTESY OF THE AUTHOR)
SAXS is a form of X-ray diffraction that focuses on small scattering angles. Scattering intensities at large angles (i.e., wide-angle X-ray scattering) contains information about small objects such as crystalline structures. Small angles contain information about large objects such as particles, macromolecules, and micelles. Figure 1 shows this inverse relation. This article will use the terms "particles," "macromolecules," and "micelles" interchangeably.

Although its name contains the word "angle," the scattering vector q is common for SAXS. Also known as momentum transfer, q reflects the process in which the X-ray photons transfer energy to the electrons with which they interact. The following equation describes the relation of the length of the scattering vector q and the scattering angle 2θ commonly used in other X-ray diffraction methods (4):

The measured intensity I as a function of the scattering vector q is given in the following equation:

The pair-distance distribution function p(r) in Equation 2 is the geometrical representation of the object in the beam. p(r) maps the distances of all electron pairs inside the particle. The scattering intensity I and the geometrical representation p(r) are related by Fourier transform.

However, representing a three-dimensional (3D) object with a one-dimensional distribution function necessarily omits some information. Converting p(r) into a three-dimensional object becomes difficult and requires additional constraints by the scientist such as connectedness or compactness.

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