Vibrational Entropy of a Protein: Large Differences between Distinct Conformations

In this article, it is investigated whether vibrational entropy (VE) is an important contribution to the free energy of globular proteins at ambient conditions. VE represents the major configurational-entropy contribution of these proteins. By definition, it is an average of the configurational entropies of the protein within single minima of the energy landscape, weighted by their occupation probabilities. Its large part originates from thermal motion of flexible torsion angles giving rise to the finite peak widths observed in torsion angle distributions. While VE may affect the equilibrium properties of proteins, it is usually neglected in numerical calculations as its consideration is difficult. Moreover, it is sometimes believed that all well-packed conformations of a globular protein have similar VE anyway. Here, we measure explicitly the VE for six different conformations from simulation data of a test protein. Estimates are obtained using the quasi-harmonic approximation for three coordinate sets, Cartesian, bond-angle-torsion (BAT), and a new set termed rotamer-degeneracy lifted BAT coordinates by us. The new set gives improved estimates as it overcomes a known shortcoming of the quasi-harmonic approximation caused by multiply populated rotamer states, and it may serve for VE estimation of macromolecules in a very general context. The obtained VE values depend considerably on the type of coordinates used. However, for all coordinate sets we find large entropy differences between the conformations, of the order of the overall stability of the protein. This result may have important implications on the choice of free energy expressions used in software for protein structure prediction, protein design, and NMR refinement.