Analysis of Calculated Normal Modes of a Set of Native and Partially Unfolded Proteins

To determine the effect on the normal modes of the multiminimum surface of the protein native state, calculations have been done for a series of conformations and different crystal structures of bovine pancreatic trypsin inhibitor (BPTI) and hen egg white lysozyme (HEWL). The conformations were generated by molecular dynamics calculations. The results indicate that the conformational space spanned by the 75 (BPTI) and 130 (HEWL) low-frequency normal modes, which account for approximately 90% of the atomic fluctuations, is relatively invariant with respect to different conformations in the native state manifold. However, the space spanned by the first three normal modes of the conformation is more variable. The overlap of the low-frequency normal modes of the native conformations with two (partially) unfolded HEWL structures is considerably lower. It is shown that averaging over the normal-mode results from an ensemble of native conformations smoothens the density of states curve and improves the agreement with inelastic neutron scattering experiments. Quantum-mechanical configurational entropies of the different structures were calculated from the normal-mode frequencies. The variation in entropy values between different crystal structures is similar to the variation between the different molecular dynamics structures. For the partially unfolded HEWL structures the entropy increased as the protein was further unfolded. To avoid biasing normal-mode calculations to a particular crystal structure and to provide error bounds, normal mode results should be averaged over a set of native conformations which can be generated by molecular dynamics.