Re-evaluation of the model-free analysis of fast internal motion in proteins using NMR relaxation

NMR spin relaxation retains a central role in the characterization of the fast internal motion of proteins and their complexes. Knowledge of the distribution and amplitude of the motion of amino acid side chains is critical for the interpretation of the dynamical proxy for the residual conformational entropy of proteins, which can potentially significantly contribute to the entropy of protein function. A popular treatment of NMR relaxation phenomena in macromolecules dissolved in liquids is the so-called model-free approach of Lipari and Szabo. The robustness of the mode-free approach has recently been strongly criticized and the remarkable range and structural context of the internal motion of proteins, characterized by such NMR relaxation techniques, attributed to artifacts arising from the model-free treatment, particularly with respect to the symmetry of the underlying motion. We develop an objective quantification of both spatial and temporal asymmetry of motion and re-examine the foundation of the model-free treatment. Concerns regarding the robustness of the model-free approach to asymmetric motion appear to be generally unwarranted. The generalized order parameter is robustly recovered. The sensitivity of the model-free treatment to asymmetric motion is restricted to the effective correlation time, which is by definition a normalized quantity and not a true time constant and therefore of much less interest in this context. With renewed confidence in the model-free approach, we then examine the microscopic distribution of side chain motion in the complex between calcium-saturated calmodulin and the calmodulin-binding domain of the endothelial nitric oxide synthase. Deuterium relaxation is used to characterize the motion of methyl groups in the complex. A remarkable range of Lipari-Szabo model-free generalized order parameters are seen with little correlation with basic structural parameters such as the depth of burial. These results are contrasted with the homologous complex with the neuronal nitric oxide synthase calmodulin-binding domain, which has distinctly different thermodynamic origins for high affinity binding.