  Some natural proteins display recurrent structural patterns. Despite being
highly similar at the tertiary structure level, repetitions within a single
repeat protein can be extremely variable at the sequence level. We propose a
mathematical definition of a repeat and investigate the occurrences of these in
different protein families. We found that long stretches of perfect repetitions
are infrequent in individual natural proteins, even for those which are known
to fold into structures of recurrent structural motifs. We found that natural
repeat proteins are indeed repetitive in their families, exhibiting abundant
stretches of 6 amino acids or longer that are perfect repetitions in the
reference family. We provide a systematic quantification for this
repetitiveness, and show that this form of repetitiveness is not exclusive of
repeat proteins, but also occurs in globular domains. A by-product of this work
is a fast classifier of proteins into families, which yields likelihood value
about a given protein belonging to a given family.
