A tool for visualizing protein motions in time-resolved crystallography

Time-resolved serial femtosecond crystallography (TR-SFX) at an x-ray free electron laser enables protein structural changes to be imaged on time-scales from femtoseconds to seconds. It can, however, be difficult to grasp the nature and timescale of global protein motions when structural changes are not isolated near a single active site. New tools are, therefore, needed to represent the global nature of electron density changes and their correlation with modeled protein structural changes. Here, we use TR-SFX data from bacteriorhodopsin to develop and validate a method for quantifying time-dependent electron density changes and correlating them throughout the protein. We define a spherical volume of difference electron density about selected atoms, average separately the positive and negative electron difference densities within each volume, and walk this spherical volume through all atoms within the protein. By correlating the resulting difference electron density amplitudes with time, our approach facilitates an initial assessment of the number and timescale of structural intermediates and highlights quake-like motions on the sub-picosecond timescale. This tool also allows structural models to be compared with experimental data using theoretical difference electron density changes calculated from refined resting and photo-activated structures.