Predicting internal protein dynamics from structures using coupled networks of hindered rotators

Internal motions in proteins, such as oscillations of internuclear vectors u(NiHiN) of amide bonds about their equilibrium position, can be characterized by a local order parameter. This dynamic parameter can be determined experimentally by measuring the longitudinal and transverse relaxation rates of N-15(i) nuclei by suitable NMR methods. In this paper, it is shown that local variations of order parameters S-ii(2) can be predicted from the knowledge of the structure. To this effect, the diffusive motion of the internuclear vector u(NiHiN) is described in a potential that takes into account the deviations of the angles theta(ij) between u(NiHiN) and neighboring vectors u(NjHjN) from their average value and similarly of deviations of the angles subtended between u(NiHiN) and u(XjYj), where X-j and Y-j are heavy atoms in the vicinity of the u(NiHiN) vector under investigation. It is shown how the concept of vicinity can be defined by a simple cutoff threshold, i.e., by neglecting vectors u(XjYj) with distances d(N-i,X-j)>7.5 angstrom. The local order parameters S-ii(2) can be predicted from the structure using a limited set of coordinates of heavy atoms. The inclusion of a larger number of heavy atoms does not improve the predictions. Applications to calmodulin, calbindin, and interleukin 4 illustrate the success and limitations of the predictions.