Structural characterization of proteins and complexes using small-angle X-ray solution scattering
Introduction
Small-angle scattering (SAS) of X-rays (SAXS) and neutrons (SANS) is a powerful method for the analysis of biological macromolecules in solution. Great progress has been made over the years in applying this technique to extract structural information from non-crystalline samples in the fields of physics, materials science and biology (Feigin and Svergun, 1987). Over the last decade, major advances in instrumentation and computational methods have led to new and exciting developments in the application of SAXS to structural biology. Active research is now being conducted by an increasing number of laboratories on advancing ab initio and rigid body modeling methods, the calculation of theoretical scattering curves from atomic models and the characterization of quaternary structure and intrinsic flexibility. In addition, advances in the automation of data collection and analysis make high throughput applications of SAXS experiments tractable (Hura et al., 2009, Round et al., 2008). Such developments have generated a renewed interest in the wider applications of the technique in the structural biology community. The present review is focused on the characterization of protein structure and complex formation, but the method is widely used for other macromolecular structures, e.g. RNA (Doniach and Lipfert, 2009, Rambo and Tainer, 2010).
Production of good quality samples is a prerequisite for a successful structural study by any method, and modern approaches to protein expression and purification used in structural biology laboratories help to facilitate this. Like the high resolution methods X-ray crystallography and nuclear magnetic resonance (NMR), SAS requires milligram amounts of highly pure, monodisperse protein that remains soluble at high concentration. However, while sample requirements are similar for the three methods (noting that an additional crystallization step is not required for the solution methods) a distinct advantage of SAXS is the speed of both data collection and sample characterization. On a modern synchrotron, scattering data can be collected in seconds, allowing an almost immediate characterization of the sample and the sample quality through the extraction of several overall parameters from the radially averaged scattering pattern. SAXS can thus be used as a method for the rapid screening of samples in various aqueous solvents/additives, including e.g. identification and optimization of crystallization conditions (Bonnete et al., 1999, Hamiaux et al., 2000).
In this review the discussion of SAS focusses on the elastic scattering of X-rays, SAXS, where dissolved macromolecules are exposed to a collimated and (for synchrotrons) focussed X-ray beam and the scattered intensity I is recorded by a detector as a function of the scattering angle (Fig. 1A). For an in-depth review of the theory behind SAXS the reader is directed to text-books and recent reviews (Feigin and Svergun, 1987, Koch et al., 2003, Putnam et al., 2007, Svergun, 2007, Svergun and Koch, 2003, Tsuruta and Irving, 2008), here some of the basic concepts will be presented with a focus on the characterization of proteins and protein complexes.
Scattering of X-rays by a solution of biomolecules is dependant on the number of biomolecules in the illuminated volume (i.e. to the solute concentration) and the excess scattering length density (often also called the contrast). For X-rays, the excess scattering length density, Δρ(r), comes from the difference in the electron density of the solute and solvent which, for biomolecules in aqueous solutions is very small. Consequently, synchrotron SAXS beamlines and laboratory sources must be optimized for the minimization of the contribution of background.
Dilute aqueous solutions of proteins, nucleic acids or other macromolecules give rise to an isotropic scattering intensity, which depends on the modulus of the momentum transfer s (s = 4πsin(θ)/λ, where 2θ is the angle between the incident and scattered beam):where the scattering amplitude A(s) is a Fourier transformation of the excess scattering length density, and the scattering intensity is average over all orientations (Ω). Following subtraction of the solvent scattering, the background corrected intensity I(s) is proportional to the scattering of a single particle averaged over all orientations.
The scattering patterns generated from a dilute solution of macromolecules are typically presented as radially averaged one-dimensional curves (Fig. 1B). From these curves several overall important parameters can be directly obtained providing information about the size, oligomeric state and overall shape of the molecule. However, advances in computational methods have now made it possible to not only extract these simple parameters, but to also determine reliable three-dimensional structures from scattering data. Low-resolution (1–2 nm) SAXS models can be determined ab initio or through the refinement of available high-resolution structures and/or homology models. While the former analysis provides a low-resolution shape of the molecule in question and often adds insight to the biological problem at hand, the latter combination of SAXS and complementary data is a powerful method for the determination of the organisation of macromolecular complexes. In addition to structure determination SAXS is routinely used for the validation of structural models, the quantitative analysis of oligomeric state and the estimation of volume fractions of components in mixtures/polydisperse systems. While SAXS has been readily employed for the analysis of flexible systems including solutions of intrinsically unfolded proteins, methods were often restricted to the determination of simple geometric parameters. A renaissance in the study of such systems by structural biologists over the last 5–10 years has led to the development of novel approaches for the analysis of flexible systems including multi-domain and intrinsically unfolded proteins (Bernado et al., 2005, Bernadó et al., 2007, Obolensky et al., 2007).
SAXS is a technique that can probe structure on an extremely broad range of macromolecular sizes (Feigin and Svergun, 1987). Small proteins and polypeptides in the range of 1–10 kDa, macromolecular complexes and large viral particles up to several hundred MDa can all be measured with modern instrumentation under near native conditions. It is often attractive to laboratory based researchers as the amount of material required for a complete study is relatively low (typically 1–2 mg protein), and almost any biologically relevant sample conditions can be used. The effect of changes to sample environment (pH, temperature, salt concentration and ligand/co-factor titration) can be easily measured and, moreover, at high-brilliance synchrotron beamlines time-resolved experiments can be conducted (Lamb et al., 2008a, Lamb et al., 2008b, Pollack and Doniach, 2009, West et al., 2008).
It should be noted here that the elastic scattering of neutrons (SANS) is also widely used to characterize macromolecular solutions. Moreover, many approaches described below for SAXS are also applicable for SANS, where the excess scattering length density (contrast) is due to the nuclear (and sometimes spin) scattering length density instead of the electron density. In SANS, samples highly absorbing to X-rays (e.g. solvents containing high salt) can be measured, and the samples will not suffer from radiation damage. Most importantly, contrast variation by hydrogen/deuterium exchange can be used yielding precious additional information about the structure of macromolecular complexes. The disadvantages to SANS are that it usually requires more material than is required for SAXS, buffer subtraction is often difficult due to the high incoherent hydrogen scattering and that the measurements cannot be done on a laboratory source. Overall, SANS is a powerful complementary tool to SAXS (Ibel and Stuhrmann, 1975, Petoukhov and Svergun, 2006, Wall et al., 2000, Whitten and Trewhella, 2009).
Section snippets
Overall SAXS parameters and rapid sample characterization
Although sophisticated approaches have now been developed for the determination of three-dimensional structure from scattering data (see the following sections), several overall invariant shape and weight parameters can be extracted directly from scattering curves enabling fast sample characterization. These parameters include: the molecular mass (MM), radius of gyration (Rg), hydrated particle volume (Vp) and maximum particle diameter (Dmax). The Guinier analysis developed by A. Guinier in the
Ab initio methods
The reconstruction of low-resolution 3D models from SAXS data alone is now a standard procedure and as such can also be considered a rapid characterization tool. The basic principles behind shape determination from 1D SAXS data were established in the 1960s, where scattering patterns were computed from different geometrical shapes and compared with experimental data. These trial-and-error methods were superseded in the 1970s through the introduction of a spherical harmonics representation by
Computation of scattering from high-resolution models
Another method for the rapid characterization of proteins and complexes if high-resolution structures or homology models are known is the computation of scattering curves from atomic models, and the comparison of these predicted curves with the experimentally determined SAXS profiles (Hough et al., 2004, King et al., 2005, Vestergaard et al., 2005). Given a model, the theoretical scattering curve can be computed and fit to the measured data, with this computation taking into account the atomic
Rigid body modeling
The assembly of macromolecular complexes can be studied through the docking of individual components into ab initio shapes (Wriggers and Chacón, 2001). However, as the resolution of SAXS derived shapes is low, it is more reliable to model the assembly of such complexes through direct refinement against the scattering data. A number of interactive and automated approaches have been developed using SAXS to determine the positions and orientations of subunits within macromolecular complexes (Boehm
Flexible systems
In the last example of the preceding section the scattering data from a multi-domain protein were successfully analyzed in terms of rigid body models, assuming therefore that all linkers were rigid such that constructs displayed no flexibility in solution. It was indeed the case for this particular protein (and it was possible to demonstrate this, see below), but very often in practice one deals with systems, which possess significant flexibility in solution.
SAXS was proven to be a powerful
Analysis of mixtures
Another important application of SAXS to rapidly characterize protein solutions is the quantitative description of mixtures (e.g. oligomeric equilibria and assembly processes). For mixtures and polydisperse solutions of non-interacting particles the resulting scattering pattern is a sum of the contributions from each component of the mixture Ik(s), weighted by the volume fraction vk of that component:
Several methods have been developed to help simplify the analysis of
Combining NMR, crystallography and SAXS
The combination of X-ray crystallography and SAXS as complementary methods is very well established. The use of SAXS to investigate the solution properties of crystal structures was pioneered in the 1970s and early 1980s, with the development of sophisticated methods for the prediction of theoretical scattering from crystal structures and initial attempts at rigid body modeling (Fedorov and Denisyuk, 1978, McDonald et al., 1979, Pavlov, 1985). These methods have been actively developed and now
Future developments
The study of biological systems using solution SAXS is increasingly gaining momentum, with many research groups looking to incorporate this technique into their research programs. As most of the SAXS analysis tools have now reached a mature state, their application is straightforward and can even be performed automatically. Therefore, not only evaluation of the overall parameters, but also shape determination, analysis of the oligomeric composition and to some extent rigid body modeling of
Acknowledgments
The authors thank their collaborators and co-workers, in particular at the EMBL (Hamburg): D. Franke, M. Gajda, C. Gorba, A. Kikhney, P. Konarev, M. Petoukhov, M Roessle, W. Shang and A. Shkumatau for many stimulating discussions and critical comments. The authors acknowledge financial support from the HFSP Grant RGP0055/2006-C. H.D.T.M is supported by a fellowship from the EMBL Interdisciplinary Postdocs programme (EIPOD).
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