Reorientational eigenmode dynamics: a combined MD/NMR relaxation analysis method for flexible parts in globular proteins

An approach is presented for the interpretation of heteronuclear NMR spin relaxation data in mobile protein parts in terms of reorientational eigenmode dynamics. The method is based on the covariance matrix of the spatial functions of the nuclear spin interactions that cause relaxation expressed as spherical harmonics of rank 2. The approach was applied to characterize the dynamics of a loop region of ubiquitin. The covariance matrix was determined from a conformational ensemble generated by a 5 ns molecular dynamics simulation. It was found that the time correlation functions of the dominant eigenmodes decay in good approximation with a single correlation time. From the reorientational eigenmodes, their eigenvalues, and correlation times, NMR relaxation data were calculated in accordance with Bloch-Wangsness-Redfield relaxation theory and directly compared with experimental (15)N relaxation parameters. Using a fitting procedure, agreement between calculated and experimental data was improved significantly by adjusting eigenvalues and correlation times of the dominant modes. The presented procedure provides detailed information on correlated reorientational dynamics of flexible parts in globular proteins. The covariance matrix was linked to the covariance matrix of backbone dihedral angle fluctuations, allowing one to study the motional behavior of these degrees of freedom on nano- and subnanosecond time scales.