The finite number of global motion patterns available to symmetric protein complexes

In PDB, more than half of the entries are structure complexes and of these complexes, most are symmetric, composed of identical subunits. Complex formation is the way through which larger structures and even molecular machines are assembled and built in nature. In this work, we apply group theory and carry out a comprehensive study of the global motion patterns of protein complexes of various symmetries. The work presents for the first time a comprehensive list of all the symmetric, aesthetically pleasing, global motion patterns available to complexes of cyclic, dihedral, tetrahedral, or octahedral symmetry. Our results clearly demonstrate that complexes with the same symmetry will have the same global motion patterns and thus may function in a similar way, and that there are only a finite number of global motion patterns available to symmetric complexes as the number of protein symmetry groups is effectively finite. The work complements our current understanding of the principle of complex formation that has been mostly structure-based by providing novel dynamics-based insights. Furthermore, as dynamics is closely tied to function, these motion patterns can provide global insights into the general functional mechanisms of protein complexes.