Symmetries of homomeric protein complexes. Complexes on the left hand side have cyclic symmetry (Cn), which means all subunits are related by rotation around a single n-fold rotation axis. Complexes on the right hand side have dihedral symmetry (Dn), which means they have an n-fold rotation axis that intersects a 2-fold rotation axis at right angles. Homomers have either symmetric face-to-face (e.g., a C2 homodimer, PDB: 1QZT), or asymmetric face-to-back interfaces (e.g., a C3 homotrimer, PDB: 1G2X, or a C4 homotetramer, PDB: 1PQF). Symmetric interfaces result in complexes with dihedral symmetry, while asymmetric interfaces imply homomeric complexes with cyclic symmetry. Symmetric interfaces evolve more readily than asymmetric ones and thus there are more dihedral than cyclic complexes (see text). During the course of evolution, proteins can evolve multiple interfaces and form higher oligomers, such as trimers of dimers (D3, PDB: 1NLS); or dimers of trimers (D3, PDB: 1V9L) or tetramers (D4, PDB: 1HAN). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]