Theoretical framework for NMR residual dipolar couplings in unfolded proteins

A theoretical framework for the prediction of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) in unfolded proteins under weakly aligning conditions is presented. The unfolded polypeptide chain is modeled as a random flight chain while the alignment medium is represented by a set of regularly arranged obstacles. For the case of bicelles oriented perpendicular to the magnetic field, a closed-form analytical result is derived. With the obtained analytical expression the RDCs are readily accessible for any locus along the chain, for chains of differing length, and for varying bicelle concentrations. The two general features predicted by the model are (i) RDCs in the center segments of a polypeptide chain are larger than RDCs in the end segments, resulting in a bell-shaped sequential distribution of RDCs, and (ii) couplings are larger for shorter chains than for longer chains at a given bicelle concentration. Experimental data available from the literature confirm the first prediction of the model, providing a tool for recognizing fully unfolded polypeptide chains. With less certainty experimental data appear to support the second prediction as well. However, more systematic experimental studies are needed in order to validate or disprove the predictions of the model. The presented framework is an important step towards a solid theoretical foundation for the analysis of experimentally measured RDCs in unfolded proteins in the case of alignment media such as polyacrylamide gels and neutral bicelle systems which align biomacromolecules by a steric mechanism. Various improvements and generalizations are possible within the suggested approach.