A perfectly symmetric lac operator binds the lac repressor very tightly.

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Abstract
A completely symmetric DNA segment has been constructed that binds the lactose repressor of Escherichia coli 10-fold more tightly than does the natural lactose operator sequence. This tight-binding operator is an inverted repeat of a 15-base-pair segment from the left half of the natural operator sequence, the inversion being about the point indicated by the arrow shown below: (sequence in text) where the upper sequence is the natural operator and the lower sequence is the symmetric operator. The increased affinity of repressor for this symmetric sequence supports the idea that the tetrameric repressor is designed for a two-module binding to DNA, presumably via two (or two pairs) of its identical subunits. The natural operator is apparently "flawed" by "incorrect" base pairs in the right operator half and by an "incorrect" spacing between the operator halves with respect to maximal repressor binding.