NMR relaxation order parameter analysis of the dynamics of protein side chains

An arbitrary multiexponential representation of the H-X bond reorientation autocorrelation function is shown to provide robust predictions of both the fast limit (S{sub f}{sup 2}) and generalized (S{sup 2}) order parameters for macromolecular NMR relaxation analysis. This representation is applied to the analysis of side-chain dynamics in Escherichia coli thioredoxin to assess correlated torsional fluctuations and the resultant configurational entropy effects. For both the high S{sup 2} phenylalanine and low S{sup 2} leucine side chains, torsional fluctuations in the major rotamer conformation can predict the observed relaxation data only if main-chain--side-chain torsional correlations are assumed.Crankshaft-like correlations occur around the side-chain {chi}{sub 2} rotation axis and the parallel main-chain rotation axis. For the sterically hindered buried side chains, torsional fluctuations are predicted to be attenuated for the main-chain rotation axis oriented gauche to the {chi}{sub 2} rotation axis. Weaker main-chain--side-chain torsional correlations appear to be present for the highly solvated mobile side chains as well. For these residues, the fast limit order parameter is interpretable in terms of fluctuations within a rotamer state, while the decrease in the order parameter due to motion near the Larmor frequencies can be used to estimate the entropy of rotamer exchange.