Temperature-dependent dynamics of the villin headpiece helical subdomain, an unusually small thermostable protein

¹⁵N spin relaxation experiments were used to measure the temperature-dependence of protein backbone conformational fluctuations in the thermostable helical subdomain, HP36, of the F-actin-binding headpiece domain of chicken villin. HP36 is the smallest domain of a naturally occurring protein that folds cooperatively to a compact native state. Spin-lattice, spin-spin, and heteronuclear nuclear Overhauser effect relaxation data for backbone amide ¹⁵N spins were collected at five temperatures in the range of 275-305 K. The data were analyzed using a model-free formalism to determine generalized order parameters, S, that describe the distribution of N-H bond vector orientations in a molecular reference frame. A novel parameter, Λ = dln(1 - S)/dln T is introduced to characterize the temperature-dependence of S. An average value of Λ = 4.5 is obtained for residues in helical conformations in HP36. This value of Λ is not reproduced by model potential energy functions commonly used to parameterize S. The maximum entropy principle was used to derive a new model potential function that reproduces both S and Λ. Contributions to the entropy, S^r, and heat capacity, C_p′^r, from reorientational conformational fluctuations were analyzed using this potential energy function. PROOF Values of S^r show a qualitative dependence on S similar to that obtained for the diffusion-in-a-cone model; however, quantitative differences of up to 0.5k, in which k is the Boltzmann constant, are observed. Values of C_p^r approach zero for small values of S and approach k for large values of S; the largest values of C_p^r are predicted to occur for intermediate values of S. The results suggest that backbone dynamics, as probed by relaxation measurements, make very little contribution to the heat capacity difference between folded and unfolded states for HP36.