Low-frequency motions in protein molecules. Beta-sheet and beta-barrel

Low-frequency internal motions in protein molecules play a key role in biological functions. Based on previous work with alpha-helical structure, the quasi-continuum model is extended to the beta-structure, another fundamental element in protein molecules. In terms of the equations derived here, one can easily calculate the low-frequency wave number of a beta-sheet in an accordionlike motion, and the low-frequency wave number of a beta-barrel in a breathing motion. The calculated results for immunoglobulin G and concanavalin A agree well with the observations. These findings further verify that the observed low-frequency motion (or the so-called dominant low-frequency mode) in a protein molecule is essentially governed by the collective fluctuations of its weak bonds, especially hydrogen bonds, and the internal displacement of the massive atoms therein, as described by the quasi-continuum model.