NMR Cross-relaxation Investigated by Molecular Dynamics Simulation: A Case Study of Ubiquitin in Solution

A one nanosecond molecular dynamics simulation of ubiquitin in solution gas been used for the calculation of the total dipolar, the radial and the reorientational correlation functions of 174 interproton NOEs and the 76 peptide chain NH vectors. The NOEs have been classified according to the structural elements they are associated with. Using multiexponential fits of the raw data spectral densities and cross-relaxation rate constants have been determined. Statistical distributions of correlation function parameters are given. On the basis of these data the assumptions underlying the standard method for distance measurement using NOE enhancements have been scrutinized. The separability of elongation and reorientation is verified for the vast majority of NOEs, but the rigid-body assumption is not supported by the simulation results. Relying on a spectral density expression that neither makes use of the product approximation not neglects spatially restricted motion, a "bias-free" (with regard to molecular motion) distance measurement method is suggested and compared with the standard method. Errors in distances up to 24% and 50% occur due to the neglect of the dispersion of order parameters and correlation times, respectively. The preconditions for a class-specific calibration method have been investigated. Within the framework of the product approximation a method for decomposing the total cross-relaxation rate constant into contribution from radial and angular motion has been developed and applied. In several cases distance fluctuation contributes significantly to cross-relaxation with both amplitude and time behaviour.