Contributions to protein entropy and heat capacity from bond vector motions measured by NMR spin relaxation

The backbone dynamics of both folded and unfolded states of staphylococcal nuclease (SNase) and the N-terminal SH3 domain from drk (drkN SH3) are studied at two different temperatures. A simple method for obtaining order parameters, describing the amplitudes of motion of bond vectors, from NMR relaxation measurements of both folded and unfolded proteins is presented and the data obtained for 15N-NH bond vectors in both the SNase and drkN SH3 systems analyzed with this approach. Using a recently developed theory relating the amplitude of bond vector motions to conformational entropy, the entropy change between the folded and unfolded forms of SNase is calculated on a per residue basis. It is noteworthy that the region of the molecule with the smallest entropy change includes those residues showing native-like structure in the unfolded form of the molecule, as established by NOE-based experiments. Order parameters of backbone 15N-NH bond vectors show significantly larger changes with temperature in the unfolded states of both proteins relative to the corresponding folded forms. The differential temperature dependence is interpreted in terms of differences in the heat capacities of folded and unfolded polypeptide chains. The contribution to the heat capacity of the unfolded chain from rapid 15N-NH bond vector motions is calculated and compared with estimates of the heat capacity of the backbone unit, -CHCONH-, obtained from calorimetric data. Methyl dynamics measured at 14 and 30 degrees C establish that the amplitudes of side-chain motions in the folded SH3 domain are more sensitive to changes in temperature than the backbone dynamics, suggesting that over this temperature range side-chain ps to ns time-scale motions contribute more to the heat capacity than backbone motions for this protein.