The Degeneracy of Protein Normal Modes

Abstract

Normal modes are frequently computed and used to portray protein dynamics and interpret conformation changes that take place during functional processes. In this work, we investigate the nature of normal modes and find that the normal modes of proteins, especially those at the low frequency range, are degenerated. The degeneracy of a mode means a mode mixes with other modes with similar frequency and vanishes under slight structural uncertainty. This work is built upon our recent discovery that the vibrational spectrum of globular proteins is universal. The high density of modes as shown in the vibrational frequency spectrum renders protein normal modes highly degeneratable, under even smallest structure uncertainty that unavoidably exists in structure determination. Indeed, we find the level of degeneracy of modes is proportional to the density of modes in the vibrational spectrum. This means that for modes at the same frequency, degeneracy is more severe for larger proteins. Degeneracy exists also in modes of coarse-grained models, but to a less extent than those of all-atom models. In closing, we discuss the implications of the degeneracy of normal modes -- how it will affect how normal modes are to be used in various normal modes-based applications.