A theory of protein dynamics to predict NMR relaxation

We present a theoretical, site-specific, approach to predict protein subunit correlation times, as measured by NMR experiments of (1)H-(15)N nuclear Overhauser effect, spin-lattice relaxation, and spin-spin relaxation. Molecular dynamics simulations are input to our equation of motion for protein dynamics, which is solved analytically to produce the eigenvalues and the eigenvectors that specify the NMR parameters. We directly compare our theoretical predictions to experiments and to simulation data for the signal transduction chemotaxis protein Y (CheY), which regulates the swimming response of motile bacteria. Our theoretical results are in good agreement with both simulations and experiments, without recourse to adjustable parameters. The theory is general, since it allows calculations of any dynamical property of interest. As an example, we present theoretical calculations of NMR order parameters and x-ray Debye-Waller temperature factors; both quantities show good agreement with experimental data.