Characterization of the Overall Rotational Diffusion of a Protein From 15N Relaxation Measurements and Hydrodynamic Calculations

In this chapter, we discuss experimental and theoretical methods for characterizing the overall rotational diffusion of molecules in solution. The methods are illustrated for the B3 domain of protein G, a small protein with rotational anisotropy of D par / D perp = 1.4. The rotational diffusion tensor of the protein is determined directly from 15 N relaxation measurements. The experimental data are treated assuming various possible models for the overall tumbling: isotropic, axially symmetric, and fully anisotropic, and the results of these analyses are compared to determine an adequate diffusion model for the protein. These experimentally derived characteristics of the protein are compared with the results of theoretical calculations of the diffusion tensor using various hydrodynamic models, to find optimal models and parameter sets for theoretical predictions. We also derive model-free characteristics of internal backbone motions in the protein, to show that different models for the overall motion can result in significantly different pictures of motion. This emphasizes the necessity of accurately characterizing the overall tumbling of a molecule to determine its local dynamics.