The Determination of Crystal Structure by X-ray Scattering Correlation Analysis

The molecular structure of materials, chemicals and bio-particles form the basis for how we understand chemical and physical interactions in the universe. The atomic structure of a molecule ultimately informs the properties and function of a material or compound. This is particularly the case for biologically active molecules, such as proteins [1]. Proteins perform many functions in nature, such as catalysis [2], cell signalling [3] or transporting nutrients [3–5]. In rational drug design, pharmaceuticals are designed to target these metabolic processes [6, 7]. Compounds are optimised based on their structure to improve binding and specificity to drug targets [8]. The most widely used method of structure determination for proteins is crystallography. In crystallography experiments, the diffraction of X-rays through a crystal is measured through all orientations of the crystal. The diffraction intensity is proportional to structure factors in the crystal structure [9] and is used to reconstruct the electron density in the crystal. Crystallography is limited by two interconnected factors. The first issue is that protein crystals must be large enough to withstand X-ray damage during rotation in the beam. X-ray damage to the crystal can cause changes to the structure within the crystal, and smaller crystals are more susceptible to X-ray damage since the X-ray dose is spread over a smaller volume [10,11]. Smaller crystals also scatter more weakly than larger crystals, because there are fewer repeating layers to enhance the diffraction signal. The requirement for large single crystals also limits what proteins can be investigated with this method. Membrane proteins are a class of protein that are situated on the cell membrane and contain hydrophilic and hydrophobic regions on the protein surface. The opposing interaction between these surfaces creates challenges in growing large crystals of membrane proteins for crystallography experiments [12]. Serial crystallography experiments, a modern iteration of traditional crystallography methods, can be used to study smaller crystals. In these experiments, a series of crystals is sequentially streamed into the X-ray beam, and diffraction from many individual crystals in random orientations is collected over time. Serial crystallography experiments are typically conducted at X-ray Free Electron Lasers (XFELs), which can study much smaller crystals than a typical synchrotron source. The femtosecond exposure of XFEL sources allows for diffraction from the crystals to be collected before their destruction [13]. The brilliance of the XFEL source, which is to the order of a billion times brighter than a typical synchrotron source [14], also means that smaller crystals can be used, which facilitates studying crystals that are challenging to grow into large single crystals. However, multi-crystal diffraction patterns are a problem within serial crystallography experiments. These occur when more than one crystal domain contributes to the diffraction pattern. In serial crystallography, this occurs when more then one crystal is imaged in the stream. In traditional crystallography, multi-crystal diffraction patterns can occur due to mosaicity in the crystal [15, 16]. Powder diffraction is another possible method of structure determination for powdered crystalline samples. Although powder diffraction is a standard tool for structure determination of small chemical crystals [17], it is rarely applied to protein crystals [18]. Protein crystal unit cells are much larger than small chemical crystals, and so diffraction peaks can overlap within the diffraction pattern. Powder diffraction also requires significantly more crystals in a powder form. This indicates a fundamental gap within protein structure determination. Serial crystallography experiments are ensemble measurements that necessitate many single diffracting crystals, while powder experiments require many thousands of crystals. Between these opposing requirements is X-ray scattering correlation analysis (XSCA). XSCA is a diffraction analysis technique that measures the diffraction from multiple scattering objects simultaneously [19], in order to calculate a scattering correlation function. In an XSCA experiment, there are no strict requirements regarding the number of scattering objects within a single diffraction pattern. However, the scattering objects must be identical, and have a uniform orientation distribution that samples all the orientations of the object. The use of XSCA for recovering single particle structure has been demonstrated for a variety of single particle structures [20–23]. The pair angle distribution function (PADF) is a quantitative measure of the distributions of two-, three-, and four-body atomic arrangements in a structure, and is calculated after performing XSCA [24]. It has been used to study the local structures in amorphous and semi-crystalline phases, such as graphitic samples [25] and liquid crystals [26] but has not yet been applied to protein crystal structures. The PADF has the potential to highlight elements of structure unique to proteins, such as alpha helices and beta sheets, and is sensitive to structural changes that would be observed when a protein changes conformation. Currently, there is no way to extract protein crystal structure factors using XSCA. Another common method of structure determination in X-ray science is phase recovery with iterative projection algorithms [27, 28]. XSCA has previously been used with iterative projection algorithms for single particle structure recovery [29,30], but is yet to be applied for crystal structure determination. By applying XSCA on protein crystal diffraction, it may be possible to recover the single crystal structure factors from multi-crystal diffraction patterns observed in serial crystallography experiments. In this thesis, I will investigate how XSCA can be used in determining protein crystal structure. This will involve determining how elements of protein structure affect components of scattering correlation functions and the PADF of crystal structures. This could lead to identifying fingerprint features in the correlation functions that inform elements of protein structure. I will also develop a novel method of extracting the reciprocal space intensity function from the scattering correlation function of a crystal. Once the intensity function has been recovered from the correlation function, established methods of crystal structure determination observed in crystallography can be used to find the atomic structure of the proteins in the crystal. Finally, I will also investigate the feasibility of XSCA experiments on crystals, and determine how many crystal diffraction patterns are required to complete the structural analysis.