Extended model free approach to analyze correlation functions of multidomain proteins in the presence of motional coupling

Interdomain motion in proteins plays an important role in biomolecular interaction. Its presence also complicates interpretation of many spectroscopy measurements. Nuclear magnetic resonance (NMR) study of domain dynamics relies on knowledge of its rotational correlation function. The extended model free (EMF) approach has been implemented to analyze coupled domain and overall motions for calmodulin, a dual-domain protein; however, the validity of EMF treatment in coupled motion has not been tested. We performed stochastic simulations on a dual-vector system employing two simple restraints to drive hydrodynamics and domain coupling: (1) both unitary vectors diffuse randomly on the surface of a sphere and (2) vectors are correlated through user-defined intervector potential. The resulting correlation curve can be adequately fit with either a single- or double-exponential decay function. The latter is consistent with the EMF treatment. The derived order parameters S (2) range from about 0.4 to 1, while the motion separation, the ratio of overall and domain motion time scales (tau m/tau s), ranges from 1 to 4. A complete overlap between time scales occurs when S (2) is less than 0.4, and the correlation function effectively behaves as a single-exponential. The S (2) values are consistent with theoretical predictions from the given potential function, differing by no more than 0.03, suggesting EMF to be a generally valid approach. In addition, from the dependence of S (2) on tau m/tau s obtained from simulation, we found a cosine potential, favoring extended conformers, as opposed to the normally assumed cone potential, reached a better agreement to experimental data.