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 confo rmations and different crystal structures of bovine pancreatic trypsin inhi bitor (BPTI) and hen egg white lysozyme (HEWL). The conformations were gene rated by molecular dynamics calculations. The results indicate that the con formational space spanned by the 75 (BPTI) and 130 (HEWL) low-frequency nor mal modes, which account for approximately 90% of the atomic fluctuations, is relatively invariant with respect to different conformations in the nati ve state manifold. However, the space spanned by the first three normal mod es of the conformation is more variable. The overlap of the low-frequency n ormal modes of the native conformations with two (partially) unfolded HEWL structures is considerably lower. It is shown that averaging over the norma l-mode results from an ensemble of native conformations smoothens the densi ty of states curve and improves the agreement with inelastic neutron scatte ring experiments. Quantum-mechanical configurational entropies of the diffe rent structures were calculated from the normal-mode frequencies. The varia tion in entropy values between different crystal structures is similar to t he variation between the different molecular dynamics structures. For the p artially 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 mo lecular dynamics.