Periodicity, planarity, and pixel (3P): a program using the intrinsic residual dipolar coupling...

We present a detailed description of a theory and a program called 3P. "3P" stands for periodicity, planarity, and pixel. The 3P program is based on the intrinsic periodic correlations between residual dipolar couplings (RDCs) and in-plane internuclear vectors, and between RDCs and the orientation of peptide planes relative to an alignment tensor. The program extracts accurate rhombic, axial components of the alignment tensor without explicit coordinates, and discrete peptide plane orientations, which are utilized in combination with readily available phi/psi angles to determine the three-dimensional backbone structures of proteins. The 3P program uses one alignment tensor. We demonstrate the utility and robustness of the program, using both experimental and synthetic data sets, which were added with different levels of noise or were incomplete. The program is interfaced to Xplor-NIH via a "3P" module and is available to the public. The limitations and differences between our program and existing methods are also discussed.