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SCOP database
SCOP heirarchy

SCOP classifies protein domains into folds, superfamilies and families.

Fold is a group of domains which are judged to have the same major secondary structures, arrangement, and topological connections.

Superfamily is a group of domains with good evidence for homology. Different superfamilies in the same fold lack evidence for homology and are therefore likely to be similar due to convergence, though homology cannot be ruled out.

Family is a group of domains with similar function.

Family and fold categories are somewhat arbitrary, because similarity of fold and similarity of function are both subjective judgments where reasonable people might disagree, especially for family where it is clear there is no dividing line between similar and dissimilar – any classification of function requires its own somewhat arbitrary hierarchy as in the Gene Ontology database.

Functions of different superfamilies in the same fold are typically so diverged as to be effectively unrelated from a genome annotation perspective.

Domain is a distinct region of a protein which is (a) believed to fold independently, (b) has a distinct functional role, and (c) belongs to a homologous group with a common ancestor. A given protein may comprise one or more domains. Roughly 70% of eukaryotic proteins have multiple domains.

Reference
Hubbard, T.J., Murzin, A.G., Brenner, S.E. and Chothia, C., 1997. SCOP: a structural classification of proteins database. Nucleic acids research, 25(1), pp.236-239.
https://doi.org/10.1093/nar/25.1.236