Small-Angle Scattering Experiments Research Articles

Visualizing and accessing correlated SAXS data sets with Similarity Maps and Simple Scattering web resources.

Constructing a comprehensive understanding of macromolecular behavior from a set of correlated small angle scattering (SAS) data is aided by tools that analyze all scattering curves together. SAS experiments on biological systems can be performed on specimens that are more easily prepared, modified, and formatted relative to those of most other techniques. An X-ray SAS measurement (SAXS) can be performed in less than a milli-second in-line with treatment steps such as purification or exposure to modifiers. These capabilities are valuable since biological macromolecules (proteins, polynucleotides, lipids, and carbohydrates) change conformation or assembly under specific conditions that often define their biological role. Furthermore, mutation or post-translational modification change their behavior and provides an avenue to tailor their mechanics. Here, we describe tools to combine multiple correlated SAS measurements for analysis and review their application to biological systems. The SAXS Similarity Map (SSM) compares a set of scattering curves and quantifies the similarity between them for display as a color on a grid. Visualizing an entire correlated data set with SSMs helps identify patterns that reveal biological functions. The SSM analysis is available as a web-based tool at https://sibyls.als.lbl.gov/saxs-similarity/. To make data available and promote tool development, we have also deployed a repository of correlated SAS data sets called Simple Scattering (available at https://simplescattering.com). The correlated data sets used to demonstrate the SSM are available on the Simple Scattering website. We expect increased utilization of correlated SAS measurements to characterize the tightly controlled mechanistic properties of biological systems and fine-tune engineered macromolecules for nanotechnology-based applications.

Reliable Biomolecular Structural Modelling with Small-Angle Scattering

The small-angle scattering (SAS) of X-rays or neutrons from biomolecules in solution can provide (1) unique structural insights, (2) information on the range of potential conformations present, (3) and powerful restraints for integrative/hybrid structural modelling (IHM). The rotational and ensemble averaging of the signal presents multiple challenges to the reliable utilisation of SAS data: (1) demonstrating SAS profile represents the species of interest, (2) reliably evaluating model fits, and (3) over-interpretation and over-fitting of data. A community driven project has been underway for more than a decade now to define the information that should be made available regarding sample quality, data acquisition and reduction, presentation of scattering data and validation, and modelling for biomolecular SAS experiments. These guidelines (Trewhella et al. (2017) Acta D73, 710) provide a reporting framework so that “readers can independently assess the quality of the data and the basis for any interpretations presented” concerning the results of bimolecular SAS experiments, including the generation or testing of 3D models. The validation task forces for SAS (Trewhella et al. (2013) Structure 21, 875) and for IHM (Sali et al. (2015) Structure 23, 1156) of the world-wide Protein Data Bank are additionally addressing the complex issues concerning the archiving and validation of IHM models that depend upon computational methods and disparate data from multiple techniques (Burley et al. (2017) Structure 25, 1317). Finally, the question of how many parameters are justified by the model evidence inherent in the SAS profile is an important question to answer when modelling conformational ensembles (Potrzebowski, Trewhella and Andr⌈ (2018) in review PLOS Computational Biology). This presentation will address the recommended reporting framework and its rationale, the reliable incorporation of SAS data in IHM, and the strengths and limits of SAS in ensemble modelling.

SAS profile correlations reveal SAS hierarchical nature and information content.

In structural biology, Small-Angle Scattering experiments (SAS) are unique, because although they provide low resolution data, they can be performed in closer-to-native conditions than those arising in X-Ray crystallography. A number of questions on SAS, however, remain unsolved, particularly in the light of modelling ensembles of conformers in solution. In this article, we study the ensemble average and covariance of SAS profiles analytically. Using this ensemble covariance, we demonstrate the hierarchical nature of SAS profiles. Furthermore, we show that the information content is not uniform and reaches its maximum in the intermediate q range. The arguments are generalized using microsecond-scale molecular dynamics trajectories of the lysozyme and on an ensemble of the intrinsically disordered protein p15PAF. We show that for highly flexible systems, the SAS profile is a representation of the ensemble of conformers in solution, and not that of one conformer in particular.

Indirect Fourier transform in the context of statistical inference.

Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments.

SAS Profile Correlations Reveal the Hierarchical Nature of SAS Data and Suggest New Scoring Strategies

In structural biology, Small-Angle Scattering experiments (SAS) are unique, because although they provide low resolution data, they can be performed in closer-to-native conditions than those arising in X-Ray crystallography. A number of questions on SAS, however, remain unsolved, particularly in the light of modelling ensembles of conformers in solution. In this letter, we study the ensemble average and covariance of SAS profiles analytically. Using this ensemble covariance, we demonstrate the hierarchical nature of SAS profiles. Furthermore, we show that the information content is not uniform and reaches its maximum in the intermediate q range. By taking into account correlated motions, we draw conclusions of profound importance to current scoring functions. We give directions for new scoring strategies, which will be valuable for very flexible systems, such as intrinsically disordered proteins.

Small Angle X-Ray and Neutron Scattering from Solutions of Biological Macromolecules. By Dmitri I. Svergun, Michel H. J. Koch, Peter A. Timmins and Roland P. May. IUCr Texts on Crystallography, No. 19. Oxford University Press, 2013. Pp. 358. Price (hardback) £49.99. ISBN: 978-0-19-963953-3.

<b>Small Angle X-Ray and Neutron Scattering from Solutions of Biological Macromolecules</b>. By Dmitri I. Svergun, Michel H. J. Koch, Peter A. Timmins and Roland P. May. IUCr Texts on Crystallography, No. 19. Oxford University Press, 2013. Pp. 358. Price (hardback) £49.99. ISBN: 978-0-19-963953-3.

Small angle scattering – moving forward

School of Biological Sciences, University of Auckland, Macromolecular , Private Bag 92-019, Auckland, New Zealand, and Argonne National Laboratory, Biosciences Division, Bldg 202, Room Q142, Argonne, IL 60439, USA One of the great strengths of crystallographic research has always been the willingness of crystallographers to work together to develop standards that will enhance both the quality and the impact of our science. This attitude, facilitated by the International Union of Crystallography (IUCr) though its various Commissions, has led to advances that have benefited much wider constituencies. A good example is the policies developed, through the IUCr, relating to the deposition and release of biological structural data (Baker et al., 1996; Baker & Saenger, 1999; Commission on Biological Macromolecules, 2000). The present issue of Acta Cryst. D highlights another such initiative in a rapidly developing area of importance to structural biology: small-angle scattering (Jacques et al., 2012). Small-angle scattering (SAS), whether of X-rays or neutrons, has been used for many years to gain structural insights into biological molecules in solution. One key advantage is obvious – you do not need crystals! In the past few years, a number of factors have come together to generate an explosion of interest in the use of SAS. New, high-quality, SAS beamlines have been developed at synchrotrons. Powerful and easy-to-use software has been developed for the interpretation of SAS data. As structural biologists tackle problems of everincreasing complexity, SAS data can be used in a variety of ways: to help interpret crystal structures by relating them to solution, to map substructures on to larger assemblies or to develop de novo information on large systems. At the same time, there are potential hazards. SAS experiments are easy to perform, and with powerful, easy-to-use software available, models are easily generated. The question then becomes one of how valid the interpretations of a particular experiment may be. On p. 620 of this issue, David Jacques, Mitchell Guss, Dmitri Svergun and Jill Trewhella take a very important step forward. They present a set of guidelines that should go a long way towards ensuring that conclusions drawn from SAS experiments can be properly assessed by readers and reviewers. These guidelines, developed through the IUCr Commission on Small-angle Scattering, consider issues such as the nature and quality of the sample, the solvent used, SAS data collection and processing protocols, the parameterization of models and the validation of results. These guidelines and the associated discussion should be read and thought about by anyone planning an SAS experiment, and will undoubtedly be of great value to researchers as the use of SAS continues to expand. It is also noteworthy that, in parallel, the Protein Data Bank has established an SAS Task Force to advise on whether models based on SAS analysis should be deposited, and, if so, with what accompanying data and what forms of validation. Meanwhile, the stage is set for continued expansion of this important technique. As Editors of a journal dedicated to biological structure and structural methods we welcome this initiative.

Practice of 2D data treatment in SAS

Many Small Angle Scattering experiments are one dimensional. Meanwhile the data of some experiments are 2 dimensional and the experimentalist may find advantages to make a full 2 dimensional data treatment or cannot avoid it. 2 dimensional data treatments present specific difficulties. The first one is an appropriate display of the whole data and of the most important part of them, in a way significant for the scientist. The second difficulty comes from the bad statistics of data which cannot be grouped together. In the following paper we describe various solutions to these problems, developed through a very long practice in LLB (Saclay, France) and SzFKI (Budapest, Hungary).

Characterizing flexible and intrinsically unstructured biological macromolecules by SAS using the Porod-Debye law.

Unstructured proteins, RNA or DNA components provide functionally important flexibility that is key to many macromolecular assemblies throughout cell biology. As objective, quantitative experimental measures of flexibility and disorder in solution are limited, small angle scattering (SAS), and in particular small angle X-ray scattering (SAXS), provides a critical technology to assess macromolecular flexibility as well as shape and assembly. Here, we consider the Porod-Debye law as a powerful tool for detecting biopolymer flexibility in SAS experiments. We show that the Porod-Debye region fundamentally describes the nature of the scattering intensity decay by capturing the information needed for distinguishing between folded and flexible particles. Particularly for comparative SAS experiments, application of the law, as described here, can distinguish between discrete conformational changes and localized flexibility relevant to molecular recognition and interaction networks. This approach aids insightful analyses of fully and partly flexible macromolecules that is more robust and conclusive than traditional Kratky analyses. Furthermore, we demonstrate for prototypic SAXS data that the ability to calculate particle density by the Porod-Debye criteria, as shown here, provides an objective quality assurance parameter that may prove of general use for SAXS modeling and validation.

Effect of interdomain dynamics on the structure determination of modular proteins by small-angle scattering

Multidomain proteins in which consecutive globular regions are connected by linkers are prevalent in nature (Levitt in Proc Natl Acad Sci USA 106:11079-11084, 2009). Some members of this family have largely resisted structural characterization as a result of challenges associated with their inherent flexibility. Small-angle scattering (SAS) is often the method of choice for their structural study. An extensive set of simulated data for both flexible and rigid multidomain systems was analyzed and modeled using standard protocols. This study clearly shows that SAXS profiles obtained from highly flexible proteins can be wrongly interpreted as arising from a rigid structure. In this context, it would be important to identify features from the SAXS data or from the derived structural models that indicate interdomain motions to differentiate between these two scenarios. Features of SAXS data that identify flexible proteins are: (1) general attenuation of fine structure in the scattering profiles, which becomes more dramatic in Kratky representations, and (2) a reduced number of interdomain correlation peaks in p(r) functions that also present large D (max) values and a smooth decrease to 0. When modeling this dynamically averaged SAXS data, the structures obtained present characteristic trends: (1) ab initio models display a decrease in resolution, and (2) rigid-body models present highly extended conformations with a lack of interdomain contacts. The ensemble optimization method represents an excellent strategy to identify interdomain motions unambiguously. This study provides information that should help researchers to select the best modeling strategy for the structural interpretation of SAS experiments of multidomain proteins.

ATSAS 2.1 – towards automated and web-supported small-angle scattering data analysis

Small-angle scattering (SAS) is frequently employed for screening large numbers of samples and for studying these samples under different conditions, including space- and time-resolved analysis. These measurements produce immense amounts of data, especially on modern high-flux and high-brilliance sources (e.g. third-generation synchrotrons). In biological SAS, like high-throughput macromolecular crystallography, large-scale analysis of proteins and macromolecular complexes is also emerging. Automation of data analysis becomes an indispensable prerequisite for adequate evaluation of high-throughput SAS experiments. Here a prototype of an automated data-analysis system for isotropic solution scattering based on the further development of the programs belonging to the package ATSAS 2.1 is reported. This system allows the major analysis tasks starting from the raw data processing and, for monodisperse systems, finishing with a three-dimensional model, to be performed automatically. Convenient web interfaces for the online use of individual ATSAS programs are also provided.

Probing the dynamics of instability in zeolitic materials

Zeolites collapse under modest pressure or temperature, their microporous structurestransforming into glasses of conventional density. Using in situ synchrotron radiationdiffraction methods we show how pressure and temperature-induced amorphization areequivalent processes and that these are mirrored by changes in the local structure of chargecompensating cations. Evidence for a low density amorphous phase and a high densityamorphous phase present during zeolite collapse emerges from small angle scatteringexperiments. Combining powder diffraction with increasing temperature or pressure,we find that the thermobaric characteristics for zeolite collapse have negatived T/d P slopes, consistent with increasing density during amorphization. However, this is not confinedto a single melting curve but, instead, the regime extends over a significant region ofT–P space. Moreover, zeolite amorphization involves depressurization and cavitation effectswhich can be used to set empirical boundaries for the stability of the low densityamorphous phase. Within the region of zeolite instability the pressure or temperature ofamorphization is found to be governed by the rate at which the stress is introduced—themore rapid this is, the higher the pressure or temperature the zeolite structure survives to.The temperature dependence of the rate of collapse is Arrhenian, suggesting that the initiallow density amorphous phase has the characteristics of a superstrong liquid incontrast to the fragility of a conventionally melt quenched glass. Possibilities forcreating ‘perfect glasses’ from the collapse of microporous crystals are discussed.

Simultaneous Rheology and Small-Angle Scattering Experiments on Block Copolymer Gels and Melts in Cubic Phases

A new instrument for simultaneous small-angle X-ray scattering and rheology experiments on soft solids is described. This device is based on a commercial rheometer with a shear sandwich geometry in which the sample is subjected to a planar oscillatory deformation. This instrument has been used for time-resolved small-angle X-ray scattering/rheology experiments at the Synchrotron Radiation Source, Daresbury Laboratory, England. The focus has been in particular on the effect of large-amplitude shearing on the orientation of cubic phases in gels of block copolymers formed in concentrated solutions, and on the bicontinuous cubic phase of a block copolymer melt. Representative results are presented for face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) phases in gels of poly(oxyethylene)–poly(oxybutylene) diblock copolymers, and for the bicontinuous cubic `gyroid' structure in a poly-(ethylene-alt-propylene)–poly(dimethylsiloxane) di-block copolymer melt. The orientations of the micellar b.c.c. phases in the gels and the gyroid structure (belonging to the b.c.c. space group Ia\bar 3d) following large-amplitude shearing are shown to be the same,i.e.directionally oriented crystals are produced in both cases, in which (111) directions are oriented along the shear direction.

Diffuse Interfaces and Small-Angle Scattering Intensity Behaviour

The contributions corresponding to the Porod, the oscillatory O(h−4) and the Kirste–Porod O(h−6) terms, present in the asymptotic expansion of the small-angle scattering (SAS) intensities, are numerically evaluated, in the presence of diffuse interfaces generated by different smoothing functions (Gaussian, spherical or Helfand–Tagami). It is shown that SAS experiments are generally unable to distinguish among different profiles, because any smoothing can be made to coincide with another type by scaling its thickness parameter. The oscillatory deviations are observable in the Porod plot of the intensities when the typical distance between parallel diffuse interfaces is greater than 50 A and the ratio of the thickness to this distance is less than 1/4. The same conclusion applies to the infinite-slit intensities.

Small-Angle Scattering of Heterogeneous Catalysts

A heterogeneously catalyzed reaction involves the adsorption of the reactants on the surface of the catalyst. Consequently, catalytic activity is usually strongly related to the microstructural features of the catalyst. Small-angle scattering (SAS) has been extensively used to study heterogeneous catalysts and it has been shown to provide useful information about the specific surface of the active phases. In particular, the majority of the research has dealt, and still deals, with supported metal catalysts, which are three-phase systems (support, voids and metal). Several attempts have been made experimentally and theoretically to overcome this problem and to obtain values for the three surface areas. In the first part of the paper, earlier results and recent approaches will be reviewed in order to give a general picture of the problem. In the second part, some recent results on other kinds of heterogeneous catalysts, such as sulfated zirconia, with strongly acidic properties, and functionalized silicas, will be discussed. Knowledge of the degree of smoothness of the particles (angularity) and thickness of the organic films obtained by SAS experiments can be very useful in clarifying morphological aspects of these porous systems.

An Optimization Regularization Method for Determination of Partial Structure Factors from Small-Angle Scattering Experiments

A new method is introduced for extracting partial structure factors from scattering data. For a bimodal mixture of colloidal particles, a minimum of three contrast-variation scattering experiments are necessary to determine the three partial structure factors. This determination of partial structure factors is a classically ill-posed matrix inversion. In addition to the random measurement error, there is random concentration error present in the set of scattering experiments, and composition parameters must be optimally chosen to minimize their effect on the inversion. The standard methods of least squares and regularization have been applied to the inversion, but are unable to provide physically significant solutions. Partial structure factors derived from the optimization regularization technique developed here satisfy the smoothness and physical constraints that partial structure factors must obey. This technique is effective in extracting partial structure factors from data with hard-sphere and sticky-hard-sphere interactions that contain concentration errors and wavelength-smearing effects.