The Sensitivity of the Pair-Angle Distribution Function to Protein Structure

Patrick Adams,Andrew V Martin,Tamar L Greaves,Jack Binns

doi:10.3390/cryst10090724

Abstract

The continued development of X-ray free-electron lasers and serial crystallography techniques has opened up new experimental frontiers. Nanoscale dynamical processes such as crystal growth can now be probed at unprecedented time and spatial resolutions. Pair-angle distribution function (PADF) analysis is a correlation-based technique that has the potential to extend the limits of current serial crystallography experiments, by relaxing the requirements for crystal order, size and number density per exposure. However, unlike traditional crystallographic methods, the PADF technique does not recover the electron density directly. Instead it encodes substantial information about local three-dimensional structure in the form of three- and four-body correlations. It is not yet known how protein structure maps into the many-body PADF correlations. In this paper, we explore the relationship between the PADF and protein conformation. We calculate correlations in reciprocal and real space for model systems exhibiting increasing degrees of order and secondary structural complexity, from disordered polypeptides, single alpha helices, helix bundles and finally a folded 100 kilodalton protein. These models systems inform us about the distinctive angular correlations generated by bonding, polypeptide chains, secondary structure and tertiary structure. They further indicate the potential to use angular correlations as a sensitive measure of conformation change that is complementary to existing structural analysis techniques.

Highlights

Proteins, as sophisticated macromolecular machines, are integral to complex biochemical processes such as DNA transcription, respiration, cell signalling and molecular transport
We ignore solvent molecules that are not bound to the structure, i.e., away from the protein surface as they are expected to produce a uniform background to the pair-angle distribution function (PADF) plots
The packing of many alpha helices into a unit cell of high symmetry generates complex texture of peaks in the diffuse angular regions of the PADF. It is clear from these correlation “fingerprints” that PADF plots can contain a significant amount of structural information that is not available in powder diffraction or small-angle X-ray scattering (SAXS) plots, which lack angular information

Summary

Introduction

As sophisticated macromolecular machines, are integral to complex biochemical processes such as DNA transcription, respiration, cell signalling and molecular transport. The most dominant technique in structural biology is X-ray crystallography [5,6,7], where protein crystals enhance the scattering signal at the expense of introducing artefacts due to crystal packing [8,9]. The starting point for PADF analysis are the correlations of intensities for each pair of detector pixels. For measurements of multiple dilute particles per exposure, the correlation function converges to the single particle correlation function [26]. This analysis has advantages when multiple crystals are measured. Points (q, θ ) can be restricted to the Bragg locations and the integral written as a sum over integrated Bragg peaks:

Results

Discussion

Conclusion