Conservative interpretation of small-angle X-ray scattering data from biological macromolecules

Abstract

Small-angle X-ray scattering (SAXS) has emerged as a key complementary technique in structural biology. The data can be used to calculate average structural properties such as particle size and molecular weight, generate low-resolution models, test high resolution structures and be used as input for complex, structure-based modelling. Importantly, however, the data is the product of an average across all orientations and populations of the particle of interest, leading to an enormous loss of information. Thus, analysis of SAXS data usually involves an attempt to solve an ill-posed inverse problem. Meaningful interpretation, free of over-fitting, can be extremely challenging. Indeed, the inexperienced practitioner can easily arrive at a conclusion that is only weakly supported by the experiment. In this thesis, we suggest that in order to maximize its reliability, SAXS data is best interpreted in terms of clear hypotheses based on previous data, which can be queried against the scattering in a predictable fashion. This conservative approach minimizes the impact of the inverse problem inherent in modelling from averaged data.In Chapter 1, we outline this principle in a published review, “Small-angle X-ray scattering for the discerning macromolecular crystallographer”, originally written for the community of structural biologists who may be seeking to use SAXS in support of their own experiments and published in The Australian Journal of Chemistry. We supplement this with a discussion of the theoretical basis of analysis and the assumptions inherent in the process, in Chapter 2. We then proceed in the main body of the thesis to demonstrate this principle across a series of case studies addressing both technically and biologically relevant questions, together covering the modelling of flexibility, the verification of high-resolution structures and the analysis of self-association, in plant, animal and bacterial systems.In Chapter 3, we first examine one of the most demanding modelling applications: a flexible system being described as an ensemble. We introduce methodology to test the robustness of moleculardynamics (MD)-SAXS solutions with respect to changes in the conformational pool, and find that for our test system, yeast importin-β, a range of different and sometimes mutually exclusive ensembles are able to reproduce the data equally well. We note that the extendedness and gross shape of the protein can be reasonably extracted, and that particular distributions can be ruled out with confidence. However, we show that it is not possible to infer the presence of any specific individual conformation or group of conformations.In Chapter 4, we address a technical issue relevant to all following chapters. The recent development of size-exclusion coupled SAXS (SEC-SAXS) has led to significant improvements in data quality and better control of problematic interparticle effects. However, the highly dilute and high-throughput nature of these data requires protocols and data processing decisions which have not yet been standardised. In this chapter, we review and test existing methodologies for the calculation of molecular weight across SEC-SAXS peaks, and develop methodology for repeatable evaluation of frames for averaging.We proceed in Chapters 5 and 6 to a series of cases relevant to plant innate immunity and fungal pathogenesis. This is an area dominated by transiently interacting systems highly amenable to study by SAXS. We identify two interfaces in plant TIR domains relevant to self-association and signaling, and show that the virulent effector protein, avrM, differs from its avirulent analogue AvrM by exhibiting reduced self-association and increased flexibility. Chapter five comprises an article published in Proc. Natl. Acad. Sci. U.S.A., presenting a multidisciplinary analysis of the signaling domains of several plant receptors involved in detection of fungal virulence factors.In Chapter 7, we move from host immunity to bacterial pathogenesis. We evaluate the behavior of a self-association disrupting mutant of S. flexneri WzzBSF, compare the crystal structure of Group A Streptococcus SEN to its solution state and characterize an unusual tetrameric mutant of the ADI enzyme from the same organism. We also conduct an extensive study of the solution structures of S. pneumonia AcdA and its component domains upon zinc binding, and finally analyse the self-association of Brucella TcpB as well as the behaviour of regions missing from its crystal structure.Finally, in Chapter 8, we draw together these cases to suggest principles and frameworks for conservative interpretation of scattering data alongside other, independent observations, as well as highlight challenges for the field moving forward. This work also highlights the importance of supporting crystallographic studies with solution biophysical techniques, especially in systems with transient self-association, and finally advances our understanding of several significant questions in protein systems involved in infection and immunity.