R-factor, Free R, and Complete Cross-Validation for Dipolar Coupling Refinement of NMR Structures

NMR structure determination of macromolecules involves a minimization problem in which atomic models, subject to restraints relating to idealized covalent geometry and nonbonded contacts, are fitted to experimental observables. The latter comprise restraints between atoms separated by ≤6 A, such as NOE-derived interproton distances, torsion angles, coupling constants, and chemical shifts, as well as restraints that provide direct information on long-range order such as dipolar couplings. An expression for the dipolar coupling R-factor is derived which provides a quantitative and readily interpretable measure of the agreement between observed and calculated dipolar couplings. The dipolar R-factor expresses the ratio of the observed rms difference between observed and calculated values with that expected for a totally random distribution of vectors. The latter can be calculated exactly from the magnitude of the alignment tensor. The dipolar R-factor scales between 0 and 1, where a value of 0 indicates perfe...