Diffuse Scattering by Protein Crystals: A Molecular Picture

Abstract

Crystals consist of atoms or molecules which are periodically arranged in three dimensions. When a crystal is exposed to X-rays, this arrangement causes constructive interference of the scattered intensities (Bragg diffraction) in some directions and destructive interference everywhere else. Bragg diffraction can be used to reconstruct the atomic structure of the molecule in the crystal. However, the arrangement of molecules in a crystal is never perfectly periodic but has some degree of disorder, especially in case of flexible protein molecules. As a result, some X-ray intensity ends up outside of the Bragg peaks as a cloudy pattern, which is usually called variational diffuse scattering. It contains information about correlated motions of (parts of) proteins. Such dynamical information is important to understand protein interactions and biochemical pathways. The aim of this thesis is to model the conformational variability of proteins with an ensemble of molecules, so that they accurately describe the experimentally observed diffuse scattering, and use this model to visualise the protein dynamics we are interested in. We use the supercell approach to calculate diffuse scattering from protein dynamics. The supercell is an extended version of the crystallographic unit cell, and serves as a small crystal model in which we can apply conformational changes to protein molecules. Initially, the supercell contains identical copies of the refined protein structure. Then, we randomly apply rigid-body displacements, which are derived from the experimentally observed root-mean-square deviations in the atomic positions (B-factors), to whole molecules and to individual secondary structural segments. This creates structural variations between molecules in the supercell. Using a simplified interaction model, we swap the positions of molecules and segments such that their local environments are restored. This way, we obtain a coarse grain crystal model containing internal and whole molecule motions (responsible for variational diffuse scattering), as well as correlated motions of molecules over distances larger than the unit cell (responsible for halos). By selectively turning each of these motions on and off in our simulations, we can use this model to study their contributions to the diffuse signal. We use four case studies of lysozyme and CypA crystals to investigate if and how much internal motions contribute to the diffuse scattering, and if we can use diffuse scattering to learn about internal motions. Motions of secondary structural segments each produce a characteristic diffuse pattern of their own, but when their motions become correlated, they behave almost like a rigid body and their pattern starts to resemble that of the whole molecule. In the case of CypA, we found that internal motions are grouped into two domains which do not strongly interact with each other. For all cases, the appearance of the diffuse map is determined by halos, which can be reproduced by correlated motions of 2--3 neighbouring molecules. We found that adding internal motions to whole molecule rigid-body motions in the model changes the contrast and the intensity balance between halos and variational scattering in the simulated map, and that the diffuse signals of internal and whole molecule motions are not additive. Including internal motions always results in better agreement with the experimental data compared to simulations which only include whole molecule motions. Only in specific circumstances, it could be possible to directly observe diffuse scattering originating from internal motions. We show that such a situation could arise if proteins in a crystal exist in one of two distinct states, for example two conformations of an enzyme.