A Method to Derive Structural Information on Molecules from Residual Dipolar Coupling NMR Data

A method for structure refinement of molecules based on residual dipolar coupling (RDC) data is proposed. It calculates RDC values using rotational and molecule-internal configurational sampling instead of the common refinement procedure that is based on the approximation of the nonuniform rotational distribution of the molecule by a single alignment tensor representing the average nonuniformity of this distribution. Using rotational sampling, as is occurring in the experiment leading to observable RDCs, the method stays close to the experiment. It avoids the use of an alignment tensor and thus the assumption that the overall rotation of the molecule is decoupled from its internal motions and that the molecule be rigid. Two simple molecules, two-united-atomic ethane and a cyclooctane molecule with eight side chains, containing 24 united atoms, serve as the so-called "toy model" test systems. The method demonstrates the influence of molecular flexibility and force-field deficiencies on the outcome of structure refinement based on RDCs. For a molecule of a given size (number of atoms N_at), there must be a sufficiently large number N_RDC of measured RDC values available to allow the restraining forces to bias the overall orientation distribution of the molecule. If the ratio N_RDC/N_at gets too small, the RDC-restraining forces will either not be strong enough to change the overall rotational direction of the molecule such that the target RDC values are approximated well or will be so strong that they induce a local deformation of the molecule. In the latter case, the size or inertia of the molecule hinders a restraining-induced overall rotation and the internal structure of the molecule is not strong enough to avoid local deformation due to the restraining forces.