Structure Calculation and Reconstruction of Discrete-State Dynamics from Residual Dipolar Couplings

Residual dipolar couplings (RDCs) acquired by nuclear magnetic resonance (NMR) spectroscopy are an indispensable source of information in investigation of molecular structures and dynamics. Here, we present a comprehensive strategy for structure calculation and reconstruction of discrete-state dynamics from RDC data that is based on the singular value decomposition (SVD) method of order tensor estimation. In addition to structure determination, we provide a mechanism of producing an ensemble of conformations for the dynamical regions of a protein from RDC data. The developed methodology has been tested on simulated RDC data with ±1 Hz of error from an 83 residue α protein (PDB ID 1A1Z ) and a 213 residue α/β protein DGCR8 (PDB ID 2YT4 ). In nearly all instances, our method reproduced the structure of the protein including the conformational ensemble to within less than 2 Å. On the basis of our investigations, arc motions with more than 30° of rotation are identified as internal dynamics and are reconstructed with sufficient accuracy. Furthermore, states with relative occupancies above 20% are consistently recognized and reconstructed successfully. Arc motions with a magnitude of 15° or relative occupancy of less than 10% are consistently unrecognizable as dynamical regions within the context of ±1 Hz of error.