Contributions to conformational entropy arising from bond vector fluctuations measured from NMR-derived order parameters: application to protein folding.

The relation between order parameters derived from NMR spin relaxation experiments and the contribution to conformational entropy from ns-ps timescale bond vector dynamics is investigated by considering a number of simple models describing bond vector motion. In a few cases both classical and quantum mechanical derivations are included to establish the validity of obtaining order parameter-entropy relations using classical mechanics only. For these cases it is found that classical and quantum mechanical derivations give very similar results so long as the square of the order parameter of the bond vector is less than approximately 0.95. For a given change in order parameter, the change in conformational entropy is sensitive to the model employed, with the absolute value of the entropy change increasing with the number of degrees of freedom in the model. The entropy-order parameter profile calculated from a 1.12 ns molecular dynamics trajectory of fully hydrated Escherichia coli ribonuclease HI is well fit using a simple expression based on a model assuming bond vector diffusion in a cone, suggesting that it may well be possible to extract meaningful entropy changes reflecting changes in ps-ns time scale motions from changes in NMR-derived order parameters. Contributions to the conformational entropy change associated with a folding-unfolding transition of an SH3 domain and calculated from changes in rapid N-HN backbone dynamics are presented.