Periodicity, planarity, residual dipolar coupling, and structures

The periodic behavior of residual dipolar couplings (RDCs) arising from nucleic acid and protein secondary structures is shown to be more complex and information-rich than previously believed. We have developed a theoretical framework which allows the bond vector orientation of nucleic acids and the peptide plane orientations of protein secondary structures to be extracted from their Dipolar waves. In this article, we focus on utilizing "Dipolar waves" of peptides to extract structure information, and describe in more detail the fundamental principles of the relationship between the periodicities in structure and RDCs, the practical procedure to extract peptide plane orientation information from RDC data, and assessment of errors using Monte-Carlo simulations. We demonstrate the utility of our method for two model alpha-helices, one kinked and one curved, and as well as an irregular beta-strand.