Most proteins adopt an approximate structural symmetry. However, they have no symmetry detectable in their sequences and it is unclear for most of these proteins whether their structural symmetry originates from duplication. As one of the six popular folds (super-folds) possessing an approximate structural symmetry, the triosephosphate isomerase barrel (TIM-barrel) domain has been widely studied. Using modified recurrent quantification analysis of primary sequences, we identified the same 2-, 3-, and 4-fold symmetry pattern as their tertiary structures. This result indicates that the symmetry in tertiary structure is coded by symmetry in the primary sequence and that the TIM-barrel adopts a 2-, 3-, or 4-fold repeat pattern during evolution. This discovery will be useful for understanding the evolutionary mechanisms of this protein family and the symmetry pattern that may be a clue into the ancient origin of duplication of half-barrels or the β a unit.
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