The sensitivity of the pair-angle distribution function to protein structure

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.