Ensemble calculations of unstructured proteins constrained by RDC and PRE data: a case study of urea-denatured ubiquitin.

The detailed, quantitative characterization of unfolded proteins is a largely unresolved task due to the enormous experimental and theoretical difficulties in describing the highly dimensional space of their conformational ensembles. Recently, residual dipolar coupling (RDC) and paramagnetic relaxation enhancement (PRE) data have provided large numbers of experimental parameters on unfolded states. To obtain a minimal model of the unfolded state according to such data we have developed new modules for the use of steric alignment RDCs and PREs as constraints in ensemble structure calculations by the program XPLOR-NIH. As an example, ensemble calculations were carried out on urea-denatured ubiquitin using a total of 419 previously obtained RDCs and 253 newly determined PREs from eight cysteine mutants coupled to MTSL. The results show that only a small number of about 10 conformers is necessary to fully reproduce the experimental RDCs, PREs and average radius of gyration. C(alpha) contacts determined on a large set (400) of 10-conformer ensembles show significant (10-20%) populations of conformations that are similar to ubiquitin's A-state, i.e. corresponding to an intact native first beta-hairpin and alpha-helix as well as non-native alpha-helical conformations in the C-terminal half. Thus, methanol/acid (A-state) and urea denaturation lead to similar low energy states of the protein ensemble, presumably due to the weakening of the hydrophobic core. Similar contacts are obtained in calculations using solely RDCs or PREs. The sampling statistics of the C(alpha) contacts in the ensembles follow a simple binomial distribution. It follows that the present RDC, PRE, and computational methods allow the statistically significant detection of subconformations in the unfolded ensemble at population levels of a few percent.