Explicit treatment of force contribution from alignment tensor using overdetermined linear equations and its application in NMR structure determination

Residual dipolar coupling (RDC) provides valuable information about the orientation of each internuclear vector in a macromolecule with respect to the static magnetic field. However, structure determination utilizing RDC still remains challenging without additional restraints such as NOE. In this context, a novel approach has been developed to efficiently extract structural information from RDC by successive application of singular value decomposition (SVD) method in the course of NMR structure determination. Force contribution from the alignment tensor is rigorously formulated in the context of SVD, and assessments have been made to verify its numerical accuracy. The efficacy of this approach is illustrated by showing that RDC restraints alone can restore a distorted beta-hairpin to native-like structure using the replica-exchange molecular dynamics simulations.