Self-consistent residual dipolar coupling based model-free analysis for the robust determination of nanosecond to microsecond protein dynamics

Residual dipolar couplings (RDCs) provide information about the dynamic average orientation of inter-nuclear vectors and amplitudes of motion up to milliseconds. They complement relaxation methods, especially on a time-scale window that we have called supra-tau(c) (tau(c) < supra-tau(c) < 50 micros). Here we present a robust approach called Self-Consistent RDC-based Model-free analysis (SCRM) that delivers RDC-based order parameters-independent of the details of the structure used for alignment tensor calculation-as well as the dynamic average orientation of the inter-nuclear vectors in the protein structure in a self-consistent manner. For ubiquitin, the SCRM analysis yields an average RDC-derived order parameter of the NH vectors 0.72 +/- 0.02 compared to = 0.778 +/- 0.003 for the Lipari-Szabo order parameters, indicating that the inclusion of the supra-tau(c) window increases the averaged amplitude of mobility observed in the sub-supra-tau(c) window by about 34%. For the beta-strand spanned by residues Lys48 to Leu50, an alternating pattern of backbone NH RDC order parameter S2(rdc)(NH) = (0.59, 0.72, 0.59) was extracted. The backbone of Lys48, whose side chain is known to be involved in the poly-ubiquitylation process that leads to protein degradation, is very mobile on the supra-tau(c) time scale (S2(rdc)(NH) = 0.59 +/- 0.03), while it is inconspicuous (S2(LS)(NH)= 0.82) on the sub-tau(c) as well as on micros-ms relaxation dispersion time scales. The results of this work differ from previous RDC dynamics studies of ubiquitin in the sense that the results are essentially independent of structural noise providing a much more robust assessment of dynamic effects that underlie the RDC data.