This study presents the first application of the model-free analysis (MFA) (Meiler in J Am Chem Soc 123:6098–6107,
2001; Lakomek in J Biomol NMR 34:101–115,
2006) to methyl group RDCs measured in 13 different alignment media in order to describe their
supra-τ
c dynamics in ubiquitin. Our results indicate that methyl groups vary from rigid to very mobile with good correlation to residue
type, distance to backbone and solvent exposure, and that considerable additional dynamics are effective at rates slower than
the correlation time
τ
c. In fact, the average amplitude of motion expressed in terms of order parameters
S
2 associated with the
supra-τ
c window brings evidence to the existence of fluctuations contributing as much additional mobility as those already present
in the faster ps-ns time scale measured from relaxation data. Comparison to previous results on ubiquitin demonstrates that
the RDC-derived order parameters are dominated both by rotameric interconversions and faster libration-type motions around
equilibrium positions. They match best with those derived from a combined J-coupling and residual dipolar coupling approach
(Chou in J Am Chem Soc 125:8959–8966,
2003) taking backbone motion into account. In order to appreciate the dynamic scale of side chains over the entire protein, the
methyl group order parameters are compared to existing dynamic ensembles of ubiquitin. Of those recently published, the broadest
one, namely the EROS ensemble (Lange in Science 320:1471–1475,
2008), fits the collection of methyl group order parameters presented here best. Last, we used the MFA-derived averaged spherical
harmonics to perform highly-parameterized rotameric searches of the side chains conformation and find expanded rotamer distributions
with excellent fit to our data. These rotamer distributions suggest the presence of concerted motions along the side chains.
Keywords Dynamics - RDCs - Side chains - Methyl group - Ubiquitin - Concerted motions