Symmetry, homology, and phrasing in the recognition of helical regulatory sequences in DNA.

Regulatory regions in DNA which have been sequenced have generally been found to contain one or more axes of two-fold rotational symmetry. If this symmetry is to be maintained in the helical sequence, the axis of rotation must be aligned with one of the two dyad axes of the helix. This is equivalent to saying that the rotational symmetry of the sequence can only be seen from certain viewing points in a circuit about the helix. More surprising is the fact that new symmetrical sequence arrangements can be seen at +/- 36 degrees, +/- 72 degrees, +/- 108 degrees, and +/- 144 degrees relative to the point at which the rotational symmetry is seen. This "amplification" of symmetry suggests a three-dimensional approach to sequence analysis. A specific reading frame, suggested by the geometry of the helix, is examined with regard to its elucidation of intra- and inter-sequence homologies. Two sequences are thus identified as being recurrent in a number of different regulatory sequences.