Theory and practice of using solvent paramagnetic relaxation enhancement to characterize protein conformational dynamics

Paramagnetic relaxation enhancement (PRE) has been established as a powerful tool in NMR for investigating protein structure and dynamics. The PRE is usually measured with a paramagnetic probe covalently attached at a specific site of an otherwise diamagnetic protein. The present work provides the numerical formulation for probing protein structure and conformational dynamics based on the solvent PRE (sPRE) measurement, using two alternative approaches. An inert paramagnetic cosolute randomly collides with the protein, and the resulting sPRE manifests the relative solvent exposure of protein nuclei. To make the back-calculated sPRE values most consistent with the observed values, the protein structure is either refined against the sPRE, or an ensemble of conformers is selected from a pre-generated library using a Monte Carlo algorithm. The ensemble structure comprises either N conformers of equal occupancy, or two conformers with different relative populations. We demonstrate the sPRE method using GB1, a structurally rigid protein, and calmodulin, a protein comprising two domains and existing in open and closed states. The sPRE can be computed with a stand-alone program for rapid evaluation, or with the invocation of a module in the latest release of the structure calculation software Xplor-NIH. As a label-free method, the sPRE measurement can be readily integrated with other biophysical techniques. The current limitations of the sPRE method are also discussed, regarding accurate measurement and theoretical calculation, model selection and suitable timescale.