The importance of slow motions for protein functional loops

Loops in proteins that connect secondary structures such as alpha-helix and beta-sheet, are often on the surface and may play a critical role in some functions of a protein. The mobility of loops is central for the motional freedom and flexibility requirements of active-site loops and may play a critical role for some functions. The structures and behaviors of loops have not been studied much in the context of the whole structure and its overall motions, especially how these might be coupled. Here we investigate loop motions by using coarse-grained structures (C(α) atoms only) to solve the motions of the system by applying Lagrange equations with elastic network models to learn about which loops move in an independent fashion and which move in coordination with domain motions, faster and slower, respectively. The normal modes of the system are calculated using eigen-decomposition of the stiffness matrix. The contribution of individual modes and groups of modes is investigated for their effects on all residues in each loop by using Fourier analyses. Our results indicate overall that the motions of functional sets of loops behave in similar ways as the whole structure. But overall only a relatively few loops move in coordination with the dominant slow modes of motion, and these are often closely related to function.